# How do you solve by factoring  5n^2- 17n= -6?

May 14, 2016

$n = \frac{2}{5}$ or $n = 3$

#### Explanation:

First add $6$ to both sides to get:

$5 {n}^{2} - 17 n + 6 = 0$

Then use an AC method:

Look for a pair of factors of $A C = 5 \cdot 6 = 30$ with sum $B = 17$.

The pair $15 , 2$ works.

Use this pair to split the middle term and factor by grouping:

$5 {n}^{2} - 17 n + 6$

$= 5 {n}^{2} - 15 n - 2 n + 6$

$= \left(5 {n}^{2} - 15 n\right) - \left(2 n - 6\right)$

$= 5 n \left(n - 3\right) - 2 \left(n - 3\right)$

$= \left(5 n - 2\right) \left(n - 3\right)$

So our original equation becomes:

$\left(5 n - 2\right) \left(n - 3\right) = 0$

with solutions:

$n = \frac{2}{5}$ or $n = 3$