Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 +  26x) -  14

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4x² + 26x - 14  =   2 • (2x² + 13x - 7) 

Trying to factor by splitting the middle term

 3.2     Factoring  2x² + 13x - 7 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  +13x  its coefficient is  13 .
The last term, "the constant", is  -7 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -7 = -14 

Step-2 : Find two factors of  -14  whose sum equals the coefficient of the middle term, which is   13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  14 
                     2x² - 1x + 14x - 7

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (2x-1)
              Add up the last 2 terms, pulling out common factors :
                    7 • (2x-1)
Step-5 : Add up the four terms of step 4 :
                    (x+7)  •  (2x-1)
             Which is the desired factorization

Final result :

  2 • (2x - 1) • (x + 7)