Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22y2 +  20y) +  24

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4y² + 20y + 24  =   4 • (y² + 5y + 6) 

Trying to factor by splitting the middle term

 3.2     Factoring  y² + 5y + 6 

The first term is,  y²  its coefficient is  1 .
The middle term is,  +5y  its coefficient is  5 .
The last term, "the constant", is  +6 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 6 = 6 

Step-2 : Find two factors of  6  whose sum equals the coefficient of the middle term, which is   5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  3 
                     y² + 2y + 3y + 6

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

Final result :

  4 • (y + 3) • (y + 2)