Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5n2 +  39n) -  54

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5n²+39n-54 

The first term is,  5n²  its coefficient is  5 .
The middle term is,  +39n  its coefficient is  39 .
The last term, "the constant", is  -54 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -54 = -270 

Step-2 : Find two factors of  -270  whose sum equals the coefficient of the middle term, which is   39 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  45 
                     5n² - 6n + 45n - 54

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

Final result :

  (5n - 6) • (n + 9)