Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  2x2) -  10x) +  72

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -2x² - 10x + 72  =   -2 • (x² + 5x - 36) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² + 5x - 36 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +5x  its coefficient is  5 .
The last term, "the constant", is  -36 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -36 = -36 

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  9 
                     x² - 4x + 9x - 36

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

Final result :

  -2 • (x + 9) • (x - 4)