Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  y²-6y-7 

The first term is,  y²  its coefficient is  1 .
The middle term is,  -6y  its coefficient is  -6 .
The last term, "the constant", is  -7 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -7 = -7 

Step-2 : Find two factors of  -7  whose sum equals the coefficient of the middle term, which is   -6 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  1 
                     y² - 7y + 1y - 7

Step-4 : Add up the first 2 terms, pulling out like factors :
                    y • (y-7)
              Add up the last 2 terms, pulling out common factors :
                     1 • (y-7)
Step-5 : Add up the four terms of step 4 :
                    (y+1)  •  (y-7)
             Which is the desired factorization

Final result :

  (y + 1) • (y - 7)