Answer
$x=-\frac{3}{2}$ or $x=-\frac{1}{2}$ or $x=3$
Work Step by Step
We simplify as follows:
$(2x+3)(2x^{2}-5x-3)=0$
$(2x+3)(2x+1)(x-3)=0$
$2x+3=0$ or $2x+1=0$ or $x-3=0$
$2x=-3$ or $2x=-1$ or $x=3$
$x=-\frac{3}{2}$ or $x=-\frac{1}{2}$ or $x=3$
