Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3x2 -  x) -  24

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3x²-x-24 

The first term is,  3x²  its coefficient is  3 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  -24 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -24 = -72 

Step-2 : Find two factors of  -72  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,  -9  and  8 
                     3x² - 9x + 8x - 24

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

Final result :

  (x - 3) • (3x + 8)