Find all possible triplets (a,b,c) of positive integers with a ≤ b ≤ c satisfying this equation:
2abc = ab + bc + ca +15
1) It is obvious from inspection that either two or three of a,b,c must be odd
2) a must be less than 3.
To see this, let a = b = c = 3
Then the LHS = 54 and the RHS = 42.
Any increase in b and or c just makes the LHS increase more than the RHS.
3) It does not take long to find all solutions.