Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (((a2) -  6a) +  9) -  4 • (2a - 1)2

Step  2  :

 2.1     Evaluate :  (2a-1)2   =    4a2-4a+1 

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -15a² + 10a + 5  =   -5 • (3a² - 2a - 1) 

Trying to factor by splitting the middle term

 3.2     Factoring  3a² - 2a - 1 

The first term is,  3a²  its coefficient is  3 .
The middle term is,  -2a  its coefficient is  -2 .
The last term, "the constant", is  -1 

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

Step-2 : Find two factors of  -3  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,  -3  and  1 
                     3a² - 3a + 1a - 1

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

Final result :

  -5 • (a - 1) • (3a + 1)