When using the inspection method, which number would you add to (and subtract from) the constant term of the numerator in this expression so the polynomial in the numerator will have(x+4) as a factor?

We are looking for k in the equation

(x+4)(x+k/4) = x^2+7x+k

The left hand side expands to:
x^2+(4+k/4)x+k = x^2+7x+k

Comparing coefficients for the linear terms, we have the equation

(4+k/4)=7
Solving for k:
16+k=28
k=12

Thus the number to be subtracted is 15-k=15-12=3