A Product That Makes Zero

If two numbers multiply to zero, then one of them is zero. There is no other way to get a product of zero. 5 × 3 is 15, not zero, and 0.1 × 0.1 is 0.01, not zero. A product is zero only when one of its factors is zero.

Now look at (x - 2)(x + 5) = 0. The left side is a product and the right side is zero, so one of the two factors must be zero. Either x - 2 = 0 or x + 5 = 0. Solve each of these small equations: x = 2 or x = -5.

The zero product rule says that a product equals zero when at least one of its factors equals zero, and only then. To solve an equation with a product on one side and zero on the other, set each factor equal to zero. Then solve each of the small equations you get. For (x - 2)(x + 5) = 0, the two small equations give x = 2 or x = -5, and both are solutions of the original equation.