One Factor Is Enough

A product is zero if at least one of its factors is zero. In $\left(x-4\right)\left(x+6\right) = 0$, substitute $x = 4$. The first factor is 0 and the second factor is 10, so the product is $0\cdot 10 = 0$. 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 $\left(x-4\right)\left(x+6\right) = 0$, 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.