Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "n2"   was replaced by   "n^2". 

Step  1  :

Trying to factor by splitting the middle term

 1.1     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,  -9  and  6 
                     n² - 9n + 6n - 54

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

Final result :

  (n + 6) • (n - 9)