# How do you solve n^2 + 7n + 15 = 5 by factoring?

May 14, 2018

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

#### Explanation:

Given: ${n}^{2} + 7 n + 15 = 5$

Subtract 5 from both sides

${n}^{2} + 7 n + 10 = 0$

Note that $2 \times 5 = 10 \mathmr{and} 2 + 5 = 7$ giving:

$\left(n + 2\right) \left(n + 5\right) = 0$

Thus: $n = - 2 \mathmr{and} n = - 5$