Answer
$(3x-2)(3x+7)$
Work Step by Step
In accordance with the rules of factoring trinomials, we need to find two variables whose product is $9(-14)=-126$ and whose sum is $15x$. A little searching determines that these numbers are $-6x$ and $21x$. Therefore, we can express the middle term $15x$ as $(-6x+21x)$ and proceed to factoring by grouping:
$9x^{2}+15x-14$
=$9x^{2}-6x+21x-14$
=$3x(3x-2)+7(3x-2)$
=$(3x-2)(3x+7)$
