#### Answer

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

#### Work Step by Step

We solve with factoring by grouping:
$2x^{3}+x^{2}-18x-9=0$
$x^{2}(2x+1)-9(2x+1)=0$
$(2x+1)(x^{2}-9)=0$
$(2x+1)(x-3)(x+3)=0$
$2x+1=0$ or $x-3=0$ or $x+3=0$
$x=-\frac{1}{2}$ or $x=3$ or $x=-3$