If a, b, c, and d are different integers, find the value of a+b+c+d

If a,b,c,d are all different integers, then so are (x-a), (x-b), (x-c), and (x-d).

If their product is 25, they can only be 5, 1, -1, and -5, since these are the only integral factors of 25.

That means a=2, b=6, c=8, d=12 and a+b+c+d=28