Question 790701
12x^3 + 12x^2 - 9x = 0 
okay so first, you were correct in your assumption that we could factor a 3x out, but the rest was incorrect 

after we factor a 3x out of every term we are left with 

{{{3x (4x^2+4x-3) =0}}}  now, we ignore the 3x for now and focus on factoring the other terms

to factor 4x^2+4x-3 we look at the multiples of the first and last terms (4 and 3) and try to make them add or subtract to equal the middle term (4). Since out last term is negative this means our answer is going to involve subtraction and be in the form  (#X - #)(#X + #). 

so the factors of 4 are 1X4 2X2  
the factors of 3 are 1X3 

so we try to arrange these terms in a way that will give us back the same equation we had before when we multiply it out

{{{ (2x-1)(2x+3) }}}

 to check to make sure this is the correct order we can foil it out and make sure it matches the original, if not rearrange the terms and foil again 

now don't forget to put the 3x back up there 
so you have 
 {{{ 3x(2x-1)(2x+3) }}}