Multiple Solutions

A numerical approach.

     Suppose the search is for integer solutions.    Examining   ABC = 4 would imply that the possible values of A, B, and C would factors of 4, that is   1, 2, or 4.   Further, either all 3 values are positive or exactly two of them are negative.

Consider values of ABC = 4    and  evaluate  3A +2B - C   to see if it is equal to 3.

         

A	B	C	3A + 2B - C

1	1	4	1
1	-1	-4	5
-1	1	-4	3
-1	-1	4	-1

Continue the table  for other sets of values where ABC = 4.   There should be 24 of them for integer solutions.

 

Of course, we could explore non-integer values numerically but there would not be a table as above with a finite number of rows.