Answer
$(3x+2)(2x+5)$
Work Step by Step
In accordance with the rules of factoring trinomials, we need to find two integers whose product is $60$ and whose sum is $19$. A little searching determines that these numbers are $4$ and $15$. Therefore, we can express the middle term $19x$ as $4x+15x$ and proceed to factoring by grouping:
$6x^{2}+19x+10$
=$6x^{2}+4x+15x+10$
=$2x(3x+2)+5(3x+2)$
=$(3x+2)(2x+5)$
