Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  2x2) -  18x) -  36

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -2x² - 18x - 36  =   -2 • (x² + 9x + 18) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² + 9x + 18 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +9x  its coefficient is  9 .
The last term, "the constant", is  +18 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 18 = 18 

Step-2 : Find two factors of  18  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,  3  and  6 
                     x² + 3x + 6x + 18

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x+3)
              Add up the last 2 terms, pulling out common factors :
                    6 • (x+3)
Step-5 : Add up the four terms of step 4 :
                    (x+6)  •  (x+3)
             Which is the desired factorization

Final result :

  -2 • (x + 6) • (x + 3)