ab + c = 12

bc + a = 12

ca + b = 12

The fact that we are told there are five answers is a clue as to what they might look like. If there was a solution with a b and c all distinct, that would form 6 answers alone, so can’t be possible. If there is a solution where two of the numbers are equal and the third is different, that would account for three answers. Assuming that is the case the remaining two answers must be when all three values are the same.

The solutions are that either two of the numbers are 1 and the other is 11 (this accounts for three of the five answers), or all three are 3, or all three are -4.