Factorize:

We have:

$2 x^{2}+3 x-90$

We have to split 3 into two numbers such that their sum is 3 and their product is $(-180)$, i.e., $2 \times(-90)$.

Clearly, $-12+15=3$ and $-12 \times 15=-180$

$\therefore 2 x^{2}+3 x-90=2 x^{2}-12 x+15 x-90$

$=2 x(x-6)+15(x-6)$

$=(x-6)(2 x+15)$