Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3x2) +  48x) -  54

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6x² + 48x - 54  =   6 • (x² + 8x - 9) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² + 8x - 9 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +8x  its coefficient is  8 .
The last term, "the constant", is  -9 

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

Step-2 : Find two factors of  -9  whose sum equals the coefficient of the middle term, which is   8 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  9 
                     x² - 1x + 9x - 9

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-1)
              Add up the last 2 terms, pulling out common factors :
                    9 • (x-1)
Step-5 : Add up the four terms of step 4 :
                    (x+9)  •  (x-1)
             Which is the desired factorization

Final result :

  6 • (x + 9) • (x - 1)