Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²+5x-24 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +5x  its coefficient is  5 .
The last term, "the constant", is  -24 

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

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  8 
                     x² - 3x + 8x - 24

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

Final result :

  (x + 8) • (x - 3)