I don't know any orderly procedure to use to derive the solution.
I just started going through them until I found one that works. So
all I can give you is the answer, which is never very helpful. Sorry.
The integers are -1, -3, and -8 .
(-1) x (-3) x (-8) = (+3) x (-8) = -24
(-1 -3 -8) = (-4 -8) = -12