Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22y2 -  17y) -  15

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4y²-17y-15 

The first term is,  4y²  its coefficient is  4 .
The middle term is,  -17y  its coefficient is  -17 .
The last term, "the constant", is  -15 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -15 = -60 

Step-2 : Find two factors of  -60  whose sum equals the coefficient of the middle term, which is   -17 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  3 
                     4y² - 20y + 3y - 15

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

Final result :

  (y - 5) • (4y + 3)