Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3a2) +  9a) -  27

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6a² + 9a - 27  =   3 • (2a² + 3a - 9) 

Trying to factor by splitting the middle term

 3.2     Factoring  2a² + 3a - 9 

The first term is,  2a²  its coefficient is  2 .
The middle term is,  +3a  its coefficient is  3 .
The last term, "the constant", is  -9 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -9 = -18 

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  6 
                     2a² - 3a + 6a - 9

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

Final result :

  3 • (2a - 3) • (a + 3)