# How do you solve (4x – 3) ² – (2x – 1) ² = 0?

May 15, 2016

$x = \frac{2}{3} , 1$

#### Explanation:

The given expression i of the form ${a}^{2} - {b}^{2}$

Where $a = 4 x - 3$ and $b = 2 x - 1$

Now, $\textcolor{red}{{a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)}$

Then,
${\left(4 x - 3\right)}^{2} - {\left(2 x - 1\right)}^{2} = 0$

$\implies \left(4 x - 3 + 2 x - 1\right) \left\{4 x - 3 - \left(2 x - 1\right)\right\} = 0$

$\implies \left(6 x - 4\right) \left(4 x - 3 - 2 x + 1\right) = 0$

$\implies \left(6 x - 4\right) \left(2 x - 2\right) = 0$

$\textcolor{red}{6 x - 4 = 0}$ or $\textcolor{b l u e}{2 x - 2 = 0}$

$\textcolor{red}{6 x = 4}$ or $\textcolor{b l u e}{2 x = 2}$

$\textcolor{red}{x = \frac{4}{6}}$ or $\textcolor{b l u e}{x = \frac{2}{2}}$

$\textcolor{red}{x = \frac{2}{3}}$ or $\textcolor{b l u e}{x = 1}$