# How do you solve (x+2)^2-(x-2)^2=(x-1)^2-(x-3)^2?

Jun 5, 2017

$x = - 2$

#### Explanation:

${\left(x + 2\right)}^{2} - {\left(x - 2\right)}^{2} = {\left(x - 1\right)}^{2} - {\left(x - 3\right)}^{2}$

$\Leftrightarrow \left(x + 2 + x - 2\right) \left(x + 2 - x + 2\right) = \left(x - 1 + x - 3\right) \left(x - 1 - x + 3\right)$

or $\left(x + \cancel{2} + x - \cancel{2}\right) \left(\cancel{x} + 2 - \cancel{x} + 2\right) = \left(x - 1 + x - 3\right) \left(\cancel{x} - 1 - \cancel{x} + 3\right)$

or $2 x \times 4 = \left(2 x - 4\right) \times 2$

or $8 x = 4 x - 8$

or $8 x - 4 x = - 8$

or $4 x = - 8$

or $x = - 2$