Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3a2) -  12a) -  9

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   12a² - 12a - 9  =   3 • (4a² - 4a - 3) 

Trying to factor by splitting the middle term

 3.2     Factoring  4a² - 4a - 3 

The first term is,  4a²  its coefficient is  4 .
The middle term is,  -4a  its coefficient is  -4 .
The last term, "the constant", is  -3 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -3 = -12 

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   -4 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  2 
                     4a² - 6a + 2a - 3

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2a • (2a-3)
              Add up the last 2 terms, pulling out common factors :
                     1 • (2a-3)
Step-5 : Add up the four terms of step 4 :
                    (2a+1)  •  (2a-3)
             Which is the desired factorization

Final result :

  3 • (2a - 3) • (2a + 1)