Math problem (x+4)(x+b)=x^2+cx+6

solve for c, plz show work

(x + 4)(x + b) = x^2 + bx + 4x + 4b = x^2 + (b + 4)x + 4b

c = b + 4
6 = 4b

Solving, I get b = 3/2, c = 11/2

Substituting x = -4 produces 0 on the left, so it will produce 0 on the right. That is:

(-4)^2 + c(-4) + 6 = 0
16 - 4c + 6 = 0
4c = 22
c = 11/2