Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2x2 +  13x) -  24

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2x²+13x-24 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  +13x  its coefficient is  13 .
The last term, "the constant", is  -24 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -24 = -48 

Step-2 : Find two factors of  -48  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,  -3  and  16 
                     2x² - 3x + 16x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (2x-3)
              Add up the last 2 terms, pulling out common factors :
                    8 • (2x-3)
Step-5 : Add up the four terms of step 4 :
                    (x+8)  •  (2x-3)
             Which is the desired factorization

Final result :

  (2x - 3) • (x + 8)