# If (m-7)(n+4)=0, what is true of m or n?

Aug 14, 2014

$m = 7$ or $n = - 4$

When we have a multiplication statement equal to 0. Then we are able to use the zero factor property which means if any factor is 0, the product is also 0.

The answer is simple when you are given a multiplication statement. However, we are generally given polynomials and we must factor the polynomial in order to find the solution. For example,
${x}^{2} + 6 x + 8 = 0$ factors into $\left(x + 2\right) \left(x + 4\right) = 0$
and the answer is $x = - 2$ or $x = - 4$.

Notice that the answers specify "or", not "and". "and" is a more strict condition. "x" cannot be -2 and -4 at the same time; so technically "and" would make the answer incorrect.

In the case of your question, $m = 7$ and $n = - 4$ would not be totally incorrect since it is possible, but you would be eliminating many solutions such as $m = 7$ and $n = 2$...