Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22y2 +  7y) -  2

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4y²+7y-2 

The first term is,  4y²  its coefficient is  4 .
The middle term is,  +7y  its coefficient is  7 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -2 = -8 

Step-2 : Find two factors of  -8  whose sum equals the coefficient of the middle term, which is   7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  8 
                     4y² - 1y + 8y - 2

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

Final result :

  (4y - 1) • (y + 2)