Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2y2 -  24y) -  26

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2y² - 24y - 26  =   2 • (y² - 12y - 13) 

Trying to factor by splitting the middle term

 3.2     Factoring  y² - 12y - 13 

The first term is,  y²  its coefficient is  1 .
The middle term is,  -12y  its coefficient is  -12 .
The last term, "the constant", is  -13 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -13 = -13 

Step-2 : Find two factors of  -13  whose sum equals the coefficient of the middle term, which is   -12 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -13  and  1 
                     y² - 13y + 1y - 13

Step-4 : Add up the first 2 terms, pulling out like factors :
                    y • (y-13)
              Add up the last 2 terms, pulling out common factors :
                     1 • (y-13)
Step-5 : Add up the four terms of step 4 :
                    (y+1)  •  (y-13)
             Which is the desired factorization

Final result :

  2 • (y + 1) • (y - 13)