One Factor Is Enough

A product is zero if at least one of its factors is zero. In (x - 4)(x + 6) = 0, substitute x = 4. The first factor is 0 and the second factor is 10, so the product is 0 × 10 = 0. The second factor does not need to be zero as well.

Each case is solved on its own. In the first case, the first factor is zero, which gives x = 4. In the second case, the second factor is zero, which gives x = -6. Each of the answers, 4 and -6, makes the original equation true by itself. You can check this by substituting each one.

Solve each factor equation separately, and join the solutions with the word or. For (x - 4)(x + 6) = 0, the solutions are x = 4 or x = -6. A solution needs to make at least one factor zero. It does not need to make both factors zero.