Question 104476
You were heading in the right direction, but you didn't quite get there.


First, put the equation in the form of Ax^2 + Bx + C = 0 by moving all the terms to the left side of the equation:


4x^2 - 13x - 12 = 0


Note that A = 4, B = -13, and C = -12


Next, create your parentheses and place the variable in the proper location for solving using the FOIL method:


 (Fx + O)(Ix + L) = 0


Now comes the time consuming part.  You need to test all possible combinations of A and C until you find the combination that makes the following equations true:


 A = F x I
 C = O x L
 B =(F x L) + (O x I)


Note: 
  F x I is also known as the First two terms
  O x L is also known as the Last two terms
  (F x L) + (O x I) is also known as Outer + Inner terms


Possible test combinations for our problem are:
A = 4: Factors into 1 x 4 and 2 x 2
C = -12: Factors into 1 x -12, -1 x 12, 2 x -6, -2 x 6, 3 x -4, and -3 x 4
Note that reverse combinations should also be tried, such as (4 x 1) for A.


So let's try out a combination (Remember A = 4, B = -13, and C = -12):


 A = F x I = 1 x 4 = 4, which is correct
 C = O x L = 1 x -12 = -12, which is correct
 B = (F x L) + (O x I) = (1 x -12) + (1 x 4) = -8, which is incorrect


Try another combination:


 A = F x I = 1 x 4 = 4, which is correct
 C = O x L = -12 x 1 = -12, which is correct
 B = (F x L) + (O x I) = (1 x 1) + (-12 x 4) = -47, which is incorrect


Hmmm... This could take some time. Try another combination:


 A = F x I = 1 x 4 = 4, which is correct
 C = O x L = -4 x 3 = -12, which is correct
 B = (F x L) + (O x I) = (1 x 3) + (-4 x 4) = -13, which is correct!


Now plug the values for F, O, I and L back into the FOIL equation from above:


 (Fx + O)(Ix + L) = 0
 (1x + (-4))(4x + 3) = 0
 (x - 4)(4x + 3) = 0 


The only thing left to do is to solve for x (this is where the Zero Product Principle is used: If AB = 0, then A = 0 or B = 0. Or both could be 0.) To do this, set each expression that is inside a parenthesis equal to 0 and solve for x:


 x - 4 = 0
 x = 4


 4x + 3 = 0
 4x = -3
 x = -3/4, or -0.75


To check your answers, plug the x values found back into the original equation and see if the equation is true:


 4(4)^2 - 13(4) - 12 = 64 - 52 - 12 = 0  True!
 4(-0.75)^2 - 13(-0.75) - 12 = 2.25 + 9.75 - 12 = 0  True!


Don't get discouraged if the answer doesn't pop out at you after a few tries when you are using the FOIL method.  Just keep chugging.  As long as you don't make any mistakes, you will eventually find the answer to this type of a problem.  Happy hunting!