# How do you solve p( - 5- p ) = 6?

Mar 22, 2018

$p = - 3 \text{ or } p = - 2$

#### Explanation:

$\text{distribute and rearrange into "color(blue)"standard form}$

$\Rightarrow - 5 p - {p}^{2} = 6$

$\Rightarrow {p}^{2} + 5 p + 6 = 0 \leftarrow \textcolor{b l u e}{\text{in standard form}}$

$\text{the factors of + 6 which sum to + 5 are + 3 and + 2}$

$\Rightarrow \left(p + 3\right) \left(p + 2\right) = 0$

$\text{equate each factor to zero and solve for p}$

$p + 3 = 0 \Rightarrow p = - 3$

$p + 2 = 0 \Rightarrow p = - 2$

Mar 22, 2018

$p = - 2 \mathmr{and} - 3$

#### Explanation:

$p \left(- 5 - p\right) = 6$

Using FOIL method :

$- 5 p - {p}^{2} = 6$

${p}^{2} + 5 p + 6 = 0$

Factorization (you can also use quadratic formula and completing square):

$\left(p + 3\right) \left(p + 2\right) = 0$

$p = - 3 \mathmr{and} - 2$