Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3y2 -  12y) -  288

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3y² - 12y - 288  =   3 • (y² - 4y - 96) 

Trying to factor by splitting the middle term

 3.2     Factoring  y² - 4y - 96 

The first term is,  y²  its coefficient is  1 .
The middle term is,  -4y  its coefficient is  -4 .
The last term, "the constant", is  -96 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -96 = -96 

Step-2 : Find two factors of  -96  whose sum equals the coefficient of the middle term, which is   -4 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  8 
                     y² - 12y + 8y - 96

Step-4 : Add up the first 2 terms, pulling out like factors :
                    y • (y-12)
              Add up the last 2 terms, pulling out common factors :
                    8 • (y-12)
Step-5 : Add up the four terms of step 4 :
                    (y+8)  •  (y-12)
             Which is the desired factorization

Final result :

  3 • (y + 8) • (y - 12)