Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2n2 +  6n) -  108

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2n² + 6n - 108  =   2 • (n² + 3n - 54) 

Trying to factor by splitting the middle term

 3.2     Factoring  n² + 3n - 54 

The first term is,  n²  its coefficient is  1 .
The middle term is,  +3n  its coefficient is  3 .
The last term, "the constant", is  -54 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -54 = -54 

Step-2 : Find two factors of  -54  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,  -6  and  9 
                     n² - 6n + 9n - 54

Step-4 : Add up the first 2 terms, pulling out like factors :
                    n • (n-6)
              Add up the last 2 terms, pulling out common factors :
                    9 • (n-6)
Step-5 : Add up the four terms of step 4 :
                    (n+9)  •  (n-6)
             Which is the desired factorization

Final result :

  2 • (n + 9) • (n - 6)