Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•7x2) -  17x) -  6

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  14x²-17x-6 

The first term is,  14x²  its coefficient is  14 .
The middle term is,  -17x  its coefficient is  -17 .
The last term, "the constant", is  -6 

Step-1 : Multiply the coefficient of the first term by the constant   14 • -6 = -84 

Step-2 : Find two factors of  -84  whose sum equals the coefficient of the middle term, which is   -17 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -21  and  4 
                     14x² - 21x + 4x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :
                    7x • (2x-3)
              Add up the last 2 terms, pulling out common factors :
                    2 • (2x-3)
Step-5 : Add up the four terms of step 4 :
                    (7x+2)  •  (2x-3)
             Which is the desired factorization

Final result :

  (2x - 3) • (7x + 2)