Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3n2) -  96n) +  360

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6n² - 96n + 360  =   6 • (n² - 16n + 60) 

Trying to factor by splitting the middle term

 3.2     Factoring  n² - 16n + 60 

The first term is,  n²  its coefficient is  1 .
The middle term is,  -16n  its coefficient is  -16 .
The last term, "the constant", is  +60 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 60 = 60 

Step-2 : Find two factors of  60  whose sum equals the coefficient of the middle term, which is   -16 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  -6 
                     n² - 10n - 6n - 60

Step-4 : Add up the first 2 terms, pulling out like factors :
                    n • (n-10)
              Add up the last 2 terms, pulling out common factors :
                    6 • (n-10)
Step-5 : Add up the four terms of step 4 :
                    (n-6)  •  (n-10)
             Which is the desired factorization

Final result :

  6 • (n - 6) • (n - 10)