# 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 .

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