Solving for Inequality $\frac{12}{2x-3}<1+2x$ I am trying to solve for the following inequality:
$$\frac{12}{2x-3}<1+2x$$
In the given answer, 
$$\frac{12}{2x-3}-(1+2x)<0$$
$$\frac{-(2x+3)(2x-5)}{2x-3}<0 \rightarrow \textrm{ How do I get to this step?}$$
$$\frac{(2x+3)(2x-5)}{2x-3}>0$$
$$(2x+3)(2x-5)(2x-3)>0 \textrm{ via multiply both sides by }(2x-3)^2$$

$$ \frac{12}{2x-3} - (1-2x) = \frac{12 - (1+2x)(2x-3) }{2x-3} = \frac{ 12 - (2x-3+4x^2-6x)}{2x-3} $$ 
$$= - \frac{4x^2-4x-15}{2x-3} = - \frac{(2x+3)(2x-5)}{2x-3} $$
