Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((3•7y2) +  19y) -  2

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  21y²+19y-2 

The first term is,  21y²  its coefficient is  21 .
The middle term is,  +19y  its coefficient is  19 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   21 • -2 = -42 

Step-2 : Find two factors of  -42  whose sum equals the coefficient of the middle term, which is   19 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  21 
                     21y² - 2y + 21y - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    y • (21y-2)
              Add up the last 2 terms, pulling out common factors :
                     1 • (21y-2)
Step-5 : Add up the four terms of step 4 :
                    (y+1)  •  (21y-2)
             Which is the desired factorization

Final result :

  (21y - 2) • (y + 1)