Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3x2 -  18x) +  24

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3x² - 18x + 24  =   3 • (x² - 6x + 8) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - 6x + 8 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -6x  its coefficient is  -6 .
The last term, "the constant", is  +8 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 8 = 8 

Step-2 : Find two factors of  8  whose sum equals the coefficient of the middle term, which is   -6 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  -2 
                     x² - 4x - 2x - 8

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

Final result :

  3 • (x - 2) • (x - 4)