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Tools/Calculators/Equation Step Solver

Equation Step Solver

ReadyHow to use

Solve linear equations, quadratics, and 2×2 systems with every step shown — discriminant, formula substitution, factored form, and a live graph of the roots.

CalculatorsMath with stepsBrowser workspace

Free to use. No account, no daily limit, and no backend processing for tool input.

Loading tool…

Tip: use samples, upload, copy, download, and send-to actions inside the workspace where available.

Actions

Calculation workflow

Fast browser-side checks

Equation Step Solver runs deterministic calculations and validations locally so small checks stay instant.

InstantLocal mathNo quota

Enter the values in the workspace and review the calculated result before copying it.
Use examples or presets where available to confirm the expected input format.
Related tools below cover adjacent validation, conversion, and lookup-style workflows.

These tools are designed for low memory use because they avoid dataset profiling and file-wide analysis.

Related tools

Matrix Step CalculatorDeterminant, inverse, RREF, rank, product, transpose, and eigenvalues with every row operation animated as a step — in exact fractions.
Derivative Step CalculatorSymbolic d/dx with every rule application shown — power, product, quotient, and chain rule — plus an interactive tangent-line explorer on a live graph.
System of Linear EquationsSolve linear systems with RREF, Gauss-Jacobi, and Gauss-Seidel methods using full step-by-step tables.
Scientific CalculatorTrig, log, exp, powers — expression evaluator.
Probability LabSimulate coins, dice, cards, and the birthday paradox — the exact theoretical probability derived step by step, then verified with an animated Monte-Carlo run.
Statistics Step ExplainerDescriptive statistics, correlation, and least-squares regression where every metric expands into its full worked calculation — with histogram, box plot, and scatter charts.

Related guides

Solve Math Step by Step Online (Free)Quadratics, derivatives, matrices, probability, and statistics solved with every rule and substitution shown — learn from the work, not just the answer.
Equation Step Solver Online GuideSolve linear equations, quadratics, and 2×2 systems with every step shown — discriminant, formula substitution, factored form, and a live graph of the roots. Use Equation Step Solver in your browser with no signup, no daily limit, and no backend processing for tool input.
Derivative Step Calculator Online GuideSymbolic d/dx with every rule application shown — power, product, quotient, and chain rule — plus an interactive tangent-line explorer on a live graph. Use Derivative Step Calculator in your browser with no signup, no daily limit, and no backend processing for tool input.
Matrix Step Calculator Online GuideDeterminant, inverse, RREF, rank, product, transpose, and eigenvalues with every row operation animated as a step — in exact fractions. Use Matrix Step Calculator in your browser with no signup, no daily limit, and no backend processing for tool input.
Probability Lab Online GuideSimulate coins, dice, cards, and the birthday paradox — the exact theoretical probability derived step by step, then verified with an animated Monte-Carlo run. Use Probability Lab in your browser with no signup, no daily limit, and no backend processing for tool input.

What is Equation Step Solver?

Equation Step Solver works through linear equations, quadratics and 2×2 systems and shows every step rather than just the answer: the discriminant computed before the roots, the quadratic formula with your actual numbers substituted in, the factored form when the roots are rational, and a graph where the roots are the x-intercepts. It is built for the case where you already have the answer from the back of the book and need to find which line of your own working went wrong.

How to use Equation Step Solver

1Choose the equation type — linear, quadratic, or a 2×2 system.
2Type your equation using ordinary notation; x² can be written x^2.
3Read the steps in order — each one states the rule being applied, not just the result.
4For quadratics, check the discriminant first: its sign tells you how many real roots to expect.
5Compare the graph against your roots — the x-intercepts should match.

Features

Every step labelled with the rule that produced it
Discriminant computed and interpreted before the roots
Quadratic formula shown with your values substituted
Factored form when the roots are rational
Elimination and substitution steps for 2×2 systems
Live graph with the roots marked as x-intercepts

Common uses

Finding which line of your own working introduced an error
Checking homework before submitting it
Revising the quadratic formula and discriminant rules
Seeing the connection between algebraic roots and graph intercepts

Used by

Students
Finance teams
Operations teams
Analysts

Common errors

Dropping the sign on b when substituting into the quadratic formula — −b means the negative of whatever b is, including when b is already negative.
Treating a negative discriminant as an error: it correctly means there are no real roots, only complex ones.
Dividing both sides by an expression containing x, which can silently delete a valid root.
In a 2×2 system, concluding "no solution" when the lines are actually identical — that is infinitely many solutions, not none.

How it works

1The equation is parsed into a normalised form so coefficients can be read off reliably regardless of how you typed it.
2The solver picks a method from the structure — isolation for linear, discriminant and formula for quadratic, elimination for systems — and records each transformation as a step.
3Roots are then plotted against the function so the algebraic result and the graph can be checked against each other.

Recommended workflow

1
Differentiate the result
Take d/dx of the same expression with every rule shown.
Open tool
2
Larger systems
Solve 3×3 and beyond with row operations in exact fractions.
Open tool

Frequently asked questions

What does the discriminant tell me?: b² − 4ac. Positive means two distinct real roots, zero means one repeated root, negative means no real roots (two complex ones). Checking it first tells you what kind of answer to expect.
Why does it show a factored form only sometimes?: Factoring is only shown when the roots are rational, because that is when the factored form has clean integer or fractional coefficients. Irrational roots factor, but not into anything more readable than the roots themselves.
Can it solve equations with no solution?: Yes, and it says so. A linear equation that reduces to something like 3 = 5 has no solution; one that reduces to 0 = 0 is true for every x.
Is my working sent anywhere?: No. Everything is computed in your browser — there is no backend to send it to.

Equation type

Decimal places

Linear equation

One variable, degree 1 — terms may sit on both sides.

Type or paste the equation

1

Solution

x = -12

Graph

Each side of the equation is plotted as a line — the solution is the x-coordinate where they intersect.

Worked solution — every step

1
Match the pattern a·x + b = c·x + d
Read off the x-coefficient and the constant on each side of the equation.
3x + 5 = 2x - 7
a = 3, b = 5 (left side)
c = 2, d = -7 (right side)
2
Subtract 2x from both sides
Collect every x-term on the left: a·x - c·x = (a - c)·x = (3 - 2)·x = 1x.
3x + 5 - 2x = 2x - 7 - 2x
x + 5 = -7
3
Subtract 5 from both sides
Move the constant to the right so the variable term stands alone.
x + 5 - 5 = -7 - 5
x = -12
4
Check the answer
Substitute x = -12 back into the original equation.
Left: 3·(-12) + 5 = -31
Right: 2·(-12) - 7 = -31
Both sides equal -31 ✓