Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (23n2 +  10n) -  1272

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   8n² + 10n - 1272  =   2 • (4n² + 5n - 636) 

Trying to factor by splitting the middle term

 3.2     Factoring  4n² + 5n - 636 

The first term is,  4n²  its coefficient is  4 .
The middle term is,  +5n  its coefficient is  5 .
The last term, "the constant", is  -636 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -636 = -2544 

Step-2 : Find two factors of  -2544  whose sum equals the coefficient of the middle term, which is   5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -48  and  53 
                     4n² - 48n + 53n - 636

Step-4 : Add up the first 2 terms, pulling out like factors :
                    4n • (n-12)
              Add up the last 2 terms, pulling out common factors :
                    53 • (n-12)
Step-5 : Add up the four terms of step 4 :
                    (4n+53)  •  (n-12)
             Which is the desired factorization

Final result :

  2 • (n - 12) • (4n + 53)