# How do you solve (4a-1)(a-2)=7a-5?

Jul 16, 2016

$a = \frac{7}{2} \mathmr{and} \frac{1}{2}$

#### Explanation:

Foil the bracket on the left hand side:

$\left(\textcolor{red}{4 a} - \textcolor{b l u e}{1}\right) \left(\textcolor{\mathmr{and} a n \ge}{a} - \textcolor{p u r p \le}{2}\right) = 7 a - 5$

$\textcolor{red}{4 a} \cdot \textcolor{\mathmr{and} a n \ge}{a} - \textcolor{red}{4 a} \cdot \textcolor{p u r p \le}{2} - \textcolor{b l u e}{1} \cdot \textcolor{\mathmr{and} a n \ge}{a} + \textcolor{b l u e}{1} \cdot \textcolor{p u r p \le}{2} = 7 a - 5$

$4 {a}^{2} - 8 a - a + 2 = 7 a - 5$

$4 {a}^{2} - 16 a + 7 = 0$

$a = \frac{16 \pm \sqrt{{16}^{2} - 4 \left(4\right) \left(7\right)}}{2 \left(4\right)}$
$a = \frac{16 \pm \sqrt{16 \left(16 - 7\right)}}{8}$
$a = \frac{16 \pm 12}{8} = \frac{28}{8} \mathmr{and} \frac{4}{8}$
$\therefore a = \frac{7}{2} \mathmr{and} \frac{1}{2}$