Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  n²+201n-2556 

The first term is,  n²  its coefficient is  1 .
The middle term is,  +201n  its coefficient is  201 .
The last term, "the constant", is  -2556 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -2556 = -2556 

Step-2 : Find two factors of  -2556  whose sum equals the coefficient of the middle term, which is   201 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  213 
                     n² - 12n + 213n - 2556

Step-4 : Add up the first 2 terms, pulling out like factors :
                    n • (n-12)
              Add up the last 2 terms, pulling out common factors :
                    213 • (n-12)
Step-5 : Add up the four terms of step 4 :
                    (n+213)  •  (n-12)
             Which is the desired factorization

Final result :

  (n + 213) • (n - 12)