Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((3•5n2) -  27n) -  6

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   15n² - 27n - 6  =   3 • (5n² - 9n - 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  5n² - 9n - 2 

The first term is,  5n²  its coefficient is  5 .
The middle term is,  -9n  its coefficient is  -9 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -2 = -10 

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   -9 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  1 
                     5n² - 10n + 1n - 2

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

Final result :

  3 • (n - 2) • (5n + 1)