Factorize:

We have:

$15 x^{2}-x-28$

We have to split $(-1)$ into two numbers such that their sum is $(-1)$ and their product is $(-420)$, i.e., $15 \times(-28)$.

Clearly, $(-21)+20=-1$ and $(-21) \times 20=-420$.

$\therefore 15 x^{2}-x-28=15 x^{2}-21 x+20 x-28$

$=3 x(5 x-7)+4(5 x-7)$

$=(5 x-7)(3 x+4)$