Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (33x2 -  60x) -  32

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  27x²-60x-32 

The first term is,  27x²  its coefficient is  27 .
The middle term is,  -60x  its coefficient is  -60 .
The last term, "the constant", is  -32 

Step-1 : Multiply the coefficient of the first term by the constant   27 • -32 = -864 

Step-2 : Find two factors of  -864  whose sum equals the coefficient of the middle term, which is   -60 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -72  and  12 
                     27x² - 72x + 12x - 32

Step-4 : Add up the first 2 terms, pulling out like factors :
                    9x • (3x-8)
              Add up the last 2 terms, pulling out common factors :
                    4 • (3x-8)
Step-5 : Add up the four terms of step 4 :
                    (9x+4)  •  (3x-8)
             Which is the desired factorization

Final result :

  (3x - 8) • (9x + 4)