Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (9 - 6a) -  (23•3a2)

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -24a² - 6a + 9  =   -3 • (8a² + 2a - 3) 

Trying to factor by splitting the middle term

 3.2     Factoring  8a² + 2a - 3 

The first term is,  8a²  its coefficient is  8 .
The middle term is,  +2a  its coefficient is  2 .
The last term, "the constant", is  -3 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -3 = -24 

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   2 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  6 
                     8a² - 4a + 6a - 3

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

Final result :

  -3 • (2a - 1) • (4a + 3)