Answer
$(5x+y)(3x-2y)$
Work Step by Step
In accordance with the rules of factoring trinomials, we need to find two variables whose product is $-30x^{2}y^{2}$ and whose sum is $-7xy$. A little searching determines that these numbers are $3xy$ and $-10xy$. Therefore, we can express the middle term, $-7xy$, as $(3xy-10xy)$ and proceed to factoring by grouping:
$15x^{2}-7xy-2y^{2}$
=$15x^{2}+3xy-10xy-2y^{2}$
=$3x(5x+y)-2y(5x+y)$
=$(5x+y)(3x-2y)$
