# How do you solve (2x + 1)(x - 4) = -7?

May 26, 2015

Given $\textcolor{red}{\left(2 x + 1\right)} \textcolor{b l u e}{\left(x - 4\right)} = \textcolor{\mathmr{and} a n \ge}{- 7}$

Multiply the two terms on the left side
(for demonstration purposes I used the distributive property, but there are several ways to do this)
$\textcolor{red}{2 x} \textcolor{b l u e}{\left(x - 4\right)} + \textcolor{red}{1} \textcolor{b l u e}{\left(x - 4\right)} = \textcolor{\mathmr{and} a n \ge}{- 7}$

$2 {x}^{2} - 8 x + x - 4 = \textcolor{\mathmr{and} a n \ge}{- 7}$

$2 {x}^{2} - 7 x - 4 = \textcolor{\mathmr{and} a n \ge}{- 7}$

Rearrange all non-zero terms to the left-side
$2 {x}^{2} - 7 x + 3 = 0$

Factor the left side
$\left(2 x - 1\right) \left(x - 3\right) = 0$

State the solutions:
$x = \frac{1}{2}$ or $x = 3$