Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22y2 +  26y) +  30

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4y² + 26y + 30  =   2 • (2y² + 13y + 15) 

Trying to factor by splitting the middle term

 3.2     Factoring  2y² + 13y + 15 

The first term is,  2y²  its coefficient is  2 .
The middle term is,  +13y  its coefficient is  13 .
The last term, "the constant", is  +15 

Step-1 : Multiply the coefficient of the first term by the constant   2 • 15 = 30 

Step-2 : Find two factors of  30  whose sum equals the coefficient of the middle term, which is   13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  3  and  10 
                     2y² + 3y + 10y + 15

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

Final result :

  2 • (2y + 3) • (y + 5)