Answer
$(7a-2)(3a+1)$
Work Step by Step
In accordance with the rules of factoring trinomials, we need to find two variables whose product is $21(-2)=-42$ and whose sum is $1$. A little searching determines that these numbers are $-6$ and $7$. Therefore, we can express the middle term $a$ as $(-6a+7a)$ and proceed to factoring by grouping:
$21a^{2}+a-2$
=$21a^{2}-6a+7a-2$
=$3a(7a-2)+1(7a-2)$
=$(7a-2)(3a+1)$