Oh boy. I don't know how to solve this off the top of my head so this answer may ramble a bit as I figure it out as I go along.
At least two numbers have to be close in value, one positive and one negative, in order for a+b+c to be true
Let's see, ABC=-12
If one letter was 4, 1, and -3 they would add to 2 and multiply to -12. I got these by just trying a bunch of combinations.
I'm pretty sure these are the right numbers, but which is which we need the AB+BC+AC formula to figure out.
IF: a=4 b=1 c=-3
4 -3 -12 = -11. Wow, first try, for reals!
A equals 4. B=1. C=-3
Would other combinations work?
a=1 b=-3 c=4
-3 + -12 + 4 = -11
Yes, other combinations work as well. Well, you have your numbers and two ways they can go. Hope this helps!