# How do you solve (5n-2)(2n+5)=0?

May 9, 2016

$n = \frac{2}{5}$ and $n = - \frac{5}{2}$

#### Explanation:

To make this expression true, we have two possibilities. Either the first factor is zero (and the second factor is finite) or the second factor is zero and the first factor is finite) - since zero times any finite quantity is also zero. Therefore, we have two equations to solve:

$5 n - 2 = 0$ and $2 n + 5 = 0$

From these two we get:

$n = \frac{2}{5}$ and $n = - \frac{5}{2}$