Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 -  12x) -  27

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4x²-12x-27 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  -12x  its coefficient is  -12 .
The last term, "the constant", is  -27 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -27 = -108 

Step-2 : Find two factors of  -108  whose sum equals the coefficient of the middle term, which is   -12 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  6 
                     4x² - 18x + 6x - 27

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

Final result :

  (2x - 9) • (2x + 3)