Factorize:

We have:

$10 x^{2}-9 x-7$

We have to split $(-9)$ into two numbers such that their sum is $(-9)$ and their product is $(-70)$, i.e., $10 \times(-7)$.

Clearly, $(-14)+5=-9$ and $(-14) \times 5=-70$

$\therefore 10 x^{2}-9 x-7=10 x^{2}+5 x-14 x-7$

$=5 x(2 x+1)-7(2 x+1)$

$=(2 x+1)(5 x-7)$