Equation Solver
Type an equation with an equals sign. The solver moves everything to one side, names the rule at each step, and says plainly when an equation has no solution or is true for every value of x.
How it works
How the Equation Solver works
the part a result on its own leaves out
What solving actually does
Solving means finding every value of x that makes both sides equal. The method is always the same: apply the same operation to both sides until x stands alone. Because both sides change together, the equation stays true throughout.
Why everything moves to one side first
An equation is easiest to classify once the right side is zero. What remains on the left tells you immediately whether it is linear, quadratic, or has no x at all — and that decides which method applies before any solving begins.
Common mistakes
Common mistakes with solving equations
the errors that actually show up, not every possible slip
Changing only one side
Subtracting 7 from the left without subtracting it from the right breaks the equality. Whatever you do, do it to both sides.
Losing a solution when x is squared
x² = 9 has two answers, 3 and −3, because both square to 9. Taking only the positive root discards half the answer.
Treating no solution as a mistake
2x + 1 = 2x + 5 has no solution: the x terms cancel and leave 1 = 5, which is false. That is a complete and correct answer, not a failed attempt.
Questions
Asked often enough to answer here
answers that change how you work
What kinds of equation does this solve?
Linear and quadratic equations in one variable, with the unknown written as x. It handles terms on both sides, and reports identities and contradictions rather than returning nothing.
What does it mean when there is no solution?
The variable cancelled and left a false statement, so no value of x can work. The two sides describe parallel lines that never meet.
What if every value of x works?
Then the two sides are the same expression written differently. That is called an identity, and every number is a solution.
Why do quadratics usually have two answers?
Because squaring loses the sign: both 3 and −3 give 9. A quadratic can have two roots, one repeated root, or none at all, and the discriminant decides which.
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