Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (23x2 -  2x) -  28

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   8x² - 2x - 28  =   2 • (4x² - x - 14) 

Trying to factor by splitting the middle term

 3.2     Factoring  4x² - x - 14 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  -14 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -14 = -56 

Step-2 : Find two factors of  -56  whose sum equals the coefficient of the middle term, which is   -1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  7 
                     4x² - 8x + 7x - 14

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

Final result :

  2 • (x - 2) • (4x + 7)