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

Nov 4, 2017

$x = - \frac{1}{2} \text{ }$ or $\text{ } x = - \frac{3}{4}$

#### Explanation:

Given:

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

Note that if $x = - \frac{1}{2}$ then $\left(2 x + 1\right) = 0$ and both sides of the equation are zero. So $x = - \frac{1}{2}$ is one solution.

If $x \ne - \frac{1}{2}$ then $\left(2 x + 1\right) \ne 0$. Divide both sides of the equation by $\left(2 x + 1\right)$ to get:

$2 x + 3 = - 2 x$

Add $2 x - 3$ to both sides to get:

$4 x = - 3$

Divide both sides by $4$ to get:

$x = - \frac{3}{4}$