Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•7y2) -  41y) +  27

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  14y²-41y+27 

The first term is,  14y²  its coefficient is  14 .
The middle term is,  -41y  its coefficient is  -41 .
The last term, "the constant", is  +27 

Step-1 : Multiply the coefficient of the first term by the constant   14 • 27 = 378 

Step-2 : Find two factors of  378  whose sum equals the coefficient of the middle term, which is   -41 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -27  and  -14 
                     14y² - 27y - 14y - 27

Step-4 : Add up the first 2 terms, pulling out like factors :
                    y • (14y-27)
              Add up the last 2 terms, pulling out common factors :
                     1 • (14y-27)
Step-5 : Add up the four terms of step 4 :
                    (y-1)  •  (14y-27)
             Which is the desired factorization

Final result :

  (14y - 27) • (y - 1)