# Solving by Factoring

You can often solve an equation by factoring, using the Zero Product Rule.

The Zero Product Rule. If a product of things equals 0, then at least one of the things must equal 0.

In terms of symbols, this means that This works with a product of more than two things.

If you can get an equation into the form " ", you can apply the Zero Product Rule by factoring JUNK and setting each factor equal to 0.

Example. Solve . The solutions are and . Example. Solve .

The equation is already in " " form, and the left side is factored. The solutions are , , and . Example. Solve . The solutions are , , and . Example. Solve .

You can't use the Zero Product Rule unless you have 0 on one side of the equation. In this case, I have to move the -3 over first. Now I can factor: The solutions are and . Example. Solve .  gives . gives , or . gives .

The solutions are , , and . Example. Solve .

Warning: Don't cancel the 's from both sides! Instead, move everything to one side, then factor:  gives . gives , or .

The solutions are and . Contact information

Copyright 2016 by Bruce Ikenaga