Factorize:

We have:

$18 x^{2}+3 x-10$

We have to split 3 into two numbers such that their sum is 3 and their product is $(-180)$, i.e., $18 \times(-10)$.

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

$\therefore 18 x^{2}+3 x-10=18 x^{2}+15 x-12 x-10$

$=3 x(6 x+5)-2(6 x+5)$

$=(6 x+5)(3 x-2)$