Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  y²-60y+875 

The first term is,  y²  its coefficient is  1 .
The middle term is,  -60y  its coefficient is  -60 .
The last term, "the constant", is  +875 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 875 = 875 

Step-2 : Find two factors of  875  whose sum equals the coefficient of the middle term, which is   -60 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -35  and  -25 
                     y² - 35y - 25y - 875

Step-4 : Add up the first 2 terms, pulling out like factors :
                    y • (y-35)
              Add up the last 2 terms, pulling out common factors :
                    25 • (y-35)
Step-5 : Add up the four terms of step 4 :
                    (y-25)  •  (y-35)
             Which is the desired factorization

Final result :

  (y - 25) • (y - 35)