# How do you solve 5r^2 - 44r + 120 = -30 + 11r by factoring?

Aug 9, 2015

$r = 5 , 6$

#### Explanation:

$5 {r}^{2} - 44 r + 120 = - 30 + 11 r$
$\implies 5 {r}^{2} - 55 r + 150 = 0$ (Adding $30 - 11 r$ to both sides)
$\implies {r}^{2} - 11 r + 30 = 0$ (Dividing by 5)
$\implies {r}^{2} - 5 r - 6 r + 30 = 0$ (Noting that $30 = 5 \cdot 6$, and that $5 + 6 = 11$)
$\implies r \left(r - 5\right) - 6 \left(r - 5\right) = 0$
$\implies \left(r - 5\right) \left(r - 6\right) = 0$
$\implies r = 5$ or $r = 6$