Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3x2) -  7x) -  12

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  12x²-7x-12 

The first term is,  12x²  its coefficient is  12 .
The middle term is,  -7x  its coefficient is  -7 .
The last term, "the constant", is  -12 

Step-1 : Multiply the coefficient of the first term by the constant   12 • -12 = -144 

Step-2 : Find two factors of  -144  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -16  and  9 
                     12x² - 16x + 9x - 12

Step-4 : Add up the first 2 terms, pulling out like factors :
                    4x • (3x-4)
              Add up the last 2 terms, pulling out common factors :
                    3 • (3x-4)
Step-5 : Add up the four terms of step 4 :
                    (4x+3)  •  (3x-4)
             Which is the desired factorization

Final result :

  (3x - 4) • (4x + 3)