Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3x2) +  12x) -  144

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6x² + 12x - 144  =   6 • (x² + 2x - 24) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² + 2x - 24 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +2x  its coefficient is  2 .
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   2 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  6 
                     x² - 4x + 6x - 24

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 :
                    6 • (x-4)
Step-5 : Add up the four terms of step 4 :
                    (x+6)  •  (x-4)
             Which is the desired factorization

Final result :

  6 • (x + 6) • (x - 4)