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