Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2x2 -  9x) -  81

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2x²-9x-81 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  -9x  its coefficient is  -9 .
The last term, "the constant", is  -81 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -81 = -162 

Step-2 : Find two factors of  -162  whose sum equals the coefficient of the middle term, which is   -9 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  9 
                     2x² - 18x + 9x - 81

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

Final result :

  (x - 9) • (2x + 9)