solve the quadratic equation to obtain the solution
12*(12+4)= 12*16 =192 so that's cant be right.
the factoring of your polynomial should be (x-8)(x+12) which gives you x-8 = 0 or x+12 = 0, meaning x=8 or x=-12. Since x is a length and cant be negative the answer must be x=8.
Does it work?
8*(4+8) = 8*12 = 96!
No, it is just that your signs were backwards.
(w-8)(w+12) = w^2 + 4w - 96
(w+8)(w-12) = w^2 - 4w - 96
Notice that the first quadratic equation is the one you are working with. The second equation above is similar to the first but the middle w-term is negative when it should be positive.