Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((27 • (x3)) -  (2•3•23x2)) -  144x
 Step  2  :

Equation at the end of step  2  :

  (33x3 -  (2•3•23x2)) -  144x

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   27x³ - 138x² - 144x  =   3x • (9x² - 46x - 48) 

Trying to factor by splitting the middle term

 4.2     Factoring  9x² - 46x - 48 

The first term is,  9x²  its coefficient is  9 .
The middle term is,  -46x  its coefficient is  -46 .
The last term, "the constant", is  -48 

Step-1 : Multiply the coefficient of the first term by the constant   9 • -48 = -432 

Step-2 : Find two factors of  -432  whose sum equals the coefficient of the middle term, which is   -46 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -54  and  8 
                     9x² - 54x + 8x - 48

Step-4 : Add up the first 2 terms, pulling out like factors :
                    9x • (x-6)
              Add up the last 2 terms, pulling out common factors :
                    8 • (x-6)
Step-5 : Add up the four terms of step 4 :
                    (9x+8)  •  (x-6)
             Which is the desired factorization

Final result :

  3x • (x - 6) • (9x + 8)