3x − 7 = 2x + 5 (linear)
- 1.Subtract 2x from both sides: x − 7 = 5
- 2.Add 7 to both sides
x = 12
Verified: 3(12) − 7 = 29 and 2(12) + 5 = 29 ✓.
One box. Any equation. Solved and proven.
Linear, quadratic or a system — just type it. The engine works out which method fits, solves with named steps, and then plugs the answer back into your original equation to prove it balances.
Covered: linear equations, quadratics, 2×2 systems, simplifying and factoring. Not yet: cubics, roots, absolute values, logarithms or rearranged formulas — the solver will tell you rather than guess.
- ✓100% free — no paywall, ever
- ✓No sign-up, no app
- ✓Every answer verified before you see it
In short
An equation solver finds the value of the unknown that makes an equation true. Type a linear equation, quadratic or 2×2 system and VerifySolve routes it to the right method automatically, solves it with exact fractions, shows every step, and then verifies the answer by substituting it back into your original equation until both sides balance exactly.
The rules every equation obeys
Whatever the type, solving means doing the same thing to both sides until the unknown stands alone. These are the moves the engine makes — and names — in its steps.
Addition / subtraction property
Multiplication / division property
Zero product property
Quadratic formula
One solver, four problem types
Each example below is a different problem type — the same single box handles all of them. Tap the chips in the solver to run one.
x² − 5x + 6 = 0 (quadratic)
- 1.Factor: (x − 2)(x − 3) = 0
- 2.Zero product property: x − 2 = 0 or x − 3 = 0
x = 2 or x = 3
Verified: 4 − 10 + 6 = 0 ✓ and 9 − 15 + 6 = 0 ✓.
2x + y = 7, x − y = 2 (system)
- 1.Add the equations to eliminate y: 3x = 9
- 2.x = 3, then back-substitute: y = 1
x = 3, y = 1
Verified in both originals: 2(3) + 1 = 7 ✓ and 3 − 1 = 2 ✓.
5(x − 2) = 3x + 4 (brackets)
- 1.Expand: 5x − 10 = 3x + 4
- 2.Subtract 3x, add 10: 2x = 14
x = 7
Verified: 5(7 − 2) = 25 and 3(7) + 4 = 25 ✓.
Common mistakes — and how to dodge them
Moving a term without flipping its sign
A term that crosses the equals sign changes sign — always. 3x − 7 = 2x + 5 becomes x = 5 + 7, not 5 − 7. Writing the “do the same to both sides” step out in full makes the flip impossible to miss.
Dividing one side only
Division is a both-sides operation. From 2x = 14, dividing just the left side gives x = 14 — wrong. Every operation in our steps is applied to the whole equation, which is exactly the habit to copy.
Dropping the ± in quadratics
x² = 9 has two answers, 3 and −3. The ± in the quadratic formula is not decoration — most quadratics have two roots, and tests love asking for both.
Equation Solver — questions
What kinds of equations can this solver handle?
Linear equations in x (including brackets and fractions), quadratic equations (factoring first, then the quadratic formula, including complex roots), systems of two linear equations in x and y, and simplifying or factoring expressions. Type a system as two equations separated by a comma.
How does it know which method to use?
The engine reads the structure of your input: a comma means a system; an x² term means quadratic; a single x means linear; no equals sign means simplify or factor the expression. You never have to pick a mode — and the steps name the method being used.
What can it not solve yet?
Cubic and higher-degree equations, equations with square roots, absolute values or logarithms, and literal equations (rearranging a formula for a letter). If you type one of those, the solver says so honestly instead of returning a made-up answer.
Why does it show a verification step?
Because an answer you cannot check is just a claim. After solving, the engine substitutes the answer back into your original equation and shows both sides matching. It is the same plug-back check your teacher wants to see — done automatically, every time.
Are answers exact fractions or decimals?
Exact fractions. The engine computes with rational arithmetic throughout, so x = 7/3 is shown as 7/3. If you type decimals, they are converted to exact fractions (0.5 becomes 1/2) before solving.
Is the equation solver really free?
Yes. No sign-up, no app, no “unlock the steps” paywall. The steps and the verification are the product — they are never hidden.
Keep solving
Algebra Calculator →
The original all-in-one algebra solver with the same verified engine.
System of Equations Calculator →
Dedicated page for two equations in x and y, with the determinant formulas.
Quadratic Equation Solver →
Factoring, the formula and the discriminant — quadratics in depth.
Solve for X Calculator →
Isolating x, from one-step equations to brackets and fractions.
A note on honest use: VerifySolve is built for learning. Use the steps to understand the method, then close the tab and try one on your own — that is where the grade actually comes from. If your teacher or school has a policy on calculators, follow it.