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**ebaines** (2a+2b+5c)(3a+3b-4c)

It's a matter of trial and error, but there are few clues you can use. First notice that the coefficients for all the a and b terms are the same - that tells you that the coefficients for a and b in the factored form are most likely the same as well. The fact that all coeefficients are positive except for the c^2 term tells you that all coefficients of the factored terms are positive except for one of the c's. The factors of 6 are either 1 and 6 or 2 and 3, so try both and see where it leads.