The Question is:-
Given that $a,b,c \geq 4$ where $a,b,c$ belongs to integers $$4abc=(a+3)(b+3)(c+3)$$ Find the value of $(a+b+c).$
This question is from an olympiad-PRMO ,the question though have solutions but none is so satisfying they simply make some assumptions here and there just to get the right answer (so I would not be revealing the answer).
I also tried the question by simply just simplifying the equation but i failed to narrow down to a result
I would like to see a nice,elegant and simple solution without any assumptions...