Answer
$(x+1)(4x-7)$
Work Step by Step
In accordance with the rules of factoring trinomials, we need to find two integers whose product is $-28$ and whose sum is $-3$. A little searching determines that these numbers are $4$ and $-7$. Therefore, we can express the middle term $-3x$ as $(4x-7x)$ and proceed to factoring by grouping:
$4x^{2}-3x-7$
=$4x^{2}+4x-7x-7$
=$4x(x+1)-7(x+1)$
=$(x+1)(4x-7)$
