Question 467162
The problem is equivalent to solving a linear diophantine  equation

3x = 5y + 2, or 3x - 5y = 2.

Bezout's identity says that the equation ax + by = c having one solution (r,s) will have other solutions given by {{{x = r + (kb)/gcd(a,b)}}} and {{{y = s - (ka)/gcd(a,b)}}}, where k is from the set of all integers.

Now one solution of 3x - 5y = 2 is (-1,-1), so let r = -1 and s = -1.

Hence {{{x = -1 + (-5k)/gcd(3,-5) = -1 - 5k}}}
 and {{{y = -1 - (3k)/gcd(a,b) = -1 - 3k}}}, 
For k = -1 ==> x = 4, y = 2;
k = -2 ==> x = 9, y = 5;
k = -3 ==> x = 14, y = 8;...etc.
Therefore there are two possible solutions to the original problem, either

3*4 = 5*2 + 2 = 12, or 

3*9 = 5*5 + 2 = 27.