Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2x2 +  7x) -  247

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2x²+7x-247 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  +7x  its coefficient is  7 .
The last term, "the constant", is  -247 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -247 = -494 

Step-2 : Find two factors of  -494  whose sum equals the coefficient of the middle term, which is   7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -19  and  26 
                     2x² - 19x + 26x - 247

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (2x-19)
              Add up the last 2 terms, pulling out common factors :
                    13 • (2x-19)
Step-5 : Add up the four terms of step 4 :
                    (x+13)  •  (2x-19)
             Which is the desired factorization

Final result :

  (2x - 19) • (x + 13)