How do you factor 6a^2-a-12

Question

I need help with this problem. I do not get it. 

Answer 1

6a²-a-12 = (2a - 3)(3a + 4)

 

Nowadays factoring is taught in a way that seems to me not to give students INSIGHT.

 

The - sign before 12 indicates that the interior signs of the two binomials will DIFFER.

 

it's a matter of splitting the leading coefficient into two factors and also splitting the 12 and arranging them in ways such that the products involved in the OI parts of FOIL will differ by one (since 1 is the coefficient of the middle term of the original trinomial.  IT'S TRIAL-AND-ERROR 'JUGGLING' and one should acquire this judgmental skill and insight after lots of practice, so DO YOUR HOMEWORK.