Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3n2 -  3n) -  18

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3n² - 3n - 18  =   3 • (n² - n - 6) 

Trying to factor by splitting the middle term

 3.2     Factoring  n² - n - 6 

The first term is,  n²  its coefficient is  1 .
The middle term is,  -n  its coefficient is  -1 .
The last term, "the constant", is  -6 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -6 = -6 

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  2 
                     n² - 3n + 2n - 6

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

Final result :

  3 • (n + 2) • (n - 3)