# Solving quadratics by factorising

Writing the quadratic as two brackets equal to zero, then setting each bracket to zero to find the solutions.

Maths (school) · Part 03: Equations and formulae · Card 6 of 8 · Last updated 2026-10-19

## Analogy

Like a door with two keys: the answer opens if either bracket becomes zero.

## Example

**x^2 - 5x + 6 = 0**

(x - 2)(x - 3) = 0
x - 2 = 0 or x - 3 = 0
x = 2 or x = 3

## In practice

The two answers can show when a thrown ball is at ground level, going up and coming down.

## Practice

### Flashcards

- **Solve x^2 - 5x + 6 = 0.** x = 2 or x = 3, from (x - 2)(x - 3) = 0.

## Questions people ask

### Why must the equation equal zero first?

Because if two numbers multiply to zero, one of them must be zero. That fact only works when the product is zero. So move every term to one side first, leaving 0 on the other, before you factorise. (x - 2)(x - 3) = 12 does not mean a bracket is 12.

### Why does a quadratic have two answers?

The graph of a quadratic is a curve that can cross the x-axis in two places. Each crossing is one solution. In (x - 2)(x - 3) = 0, both x = 2 and x = 3 make a bracket zero, so both work.

## Related concepts

- [The quadratic formula](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-7)
- [Solving linear equations](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-1)
- [Unknowns on both sides](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-2)
- [Changing the subject](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-3)

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