Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3a2 +  9a) -  12

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

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

Trying to factor by splitting the middle term

 3.2     Factoring  a² + 3a - 4 

The first term is,  a²  its coefficient is  1 .
The middle term is,  +3a  its coefficient is  3 .
The last term, "the constant", is  -4 

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

Step-2 : Find two factors of  -4  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,  -1  and  4 
                     a² - 1a + 4a - 4

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

Final result :

  3 • (a + 4) • (a - 1)