Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5n2 -  8n) -  21

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5n²-8n-21 

The first term is,  5n²  its coefficient is  5 .
The middle term is,  -8n  its coefficient is  -8 .
The last term, "the constant", is  -21 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -21 = -105 

Step-2 : Find two factors of  -105  whose sum equals the coefficient of the middle term, which is   -8 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  7 
                     5n² - 15n + 7n - 21

Step-4 : Add up the first 2 terms, pulling out like factors :
                    5n • (n-3)
              Add up the last 2 terms, pulling out common factors :
                    7 • (n-3)
Step-5 : Add up the four terms of step 4 :
                    (5n+7)  •  (n-3)
             Which is the desired factorization

Final result :

  (n - 3) • (5n + 7)