Factoring is a method that can be used to solve equations of a degree higher than 1. This method uses the zero product rule.

If ( *a*)( *b*) = 0, then

Either ( *a*) = 0, ( *b*) = 0, or both.

##### Example 1

Solve *x*( *x* + 3) = 0.

*x*( *x* + 3) = 0

Apply the zero product rule.

Check the solution.

The solution is *x* = 0 or *x* = –3.

##### Example 2

Solve *x* ^{2} – 5 *x* + 6 = 0.

*x* ^{2} – 5 *x* + 6 = 0

Factor.

( *x* – 2)( *x* – 3) = 0

Apply the zero product rule.

The check is left to you. The solution is *x* = 2 or *x* = 3.

##### Example 3

Solve 3 *x*(2 *x* – 5) = –4(4 *x* – 3).

3 *x*(2 *x* – 5) = –4(4 *x* – 3)

Distribute.

6 *x* ^{2} – 15 *x* = –16 *x* + 12

Get all terms on one side, leaving zero on the other, in order to apply the zero product rule.

6 *x* ^{2} + *x* – 12 = 0

Factor.

(3 *x* – 4)(2 *x* + 3) = 0

Apply the zero product rule.

The check is left to you. The solution is or .

##### Example 4

Solve 2 *y* ^{3} = 162 *y*.

2 *y* ^{3} = 162 *y*

Get all terms on one side of the equation.

2 *y* ^{3} – 162 *y* = 0

Factor (GCF).

2 *y*( *y* ^{2} – 81) = 0

Continue to factor (difference of squares).

2 *y*( *y* + 9)( *y* – 9) = 0

Apply the zero product rule.

The check is left to *y*ou. The solution is *y* = 0 or *y* = –9 or *y* = 9.