The idea
When a product is zero, at least one factor must be zero. This lets you turn a factorised quadratic equation into two linear equations. First rearrange the equation so one side is zero.
Before you begin: Expand two brackets and work with positive and negative factors.
Find both solutions of the quadratic equation.
Find two integers whose product is −6 and whose sum is 1. They are 3 and −2.
Use that pair to factorise. Expanding the brackets checks the middle term.
Set each factor equal to zero. Either factor can make the product zero.
Both solutions satisfy the original equation. Keep both values.
A mistake to avoid
The zero-product rule only applies when the product equals zero. Also, the signs inside the brackets are opposite to the corresponding roots.
Your turn.
Find both solutions.
Show the solution
The required pair has product 6 and sum −5. Both factors must be considered.