Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22n2 -  15n) -  25

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4n²-15n-25 

The first term is,  4n²  its coefficient is  4 .
The middle term is,  -15n  its coefficient is  -15 .
The last term, "the constant", is  -25 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -25 = -100 

Step-2 : Find two factors of  -100  whose sum equals the coefficient of the middle term, which is   -15 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  5 
                     4n² - 20n + 5n - 25

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

Final result :

  (n - 5) • (4n + 5)