Evaluate: 2x^3+x^2-18x-9=0

Expression: $2x^{3}+x^{2}-18x-9=0$

Factor $2x^{3}+x^{2}-18x-9:{\quad}(2x+1)(x+3)(x-3)$

$(2x+1)(x+3)(x-3)=0$

Using the Zero Factor Principle:\quad If $ ab=0 $then $ a=0 $or $ b=0$

$2x+1=0\lor x+3=0\lor x-3=0$

The solutions are

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