Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  (23•3x2)) +  20x) +  100

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -24x² + 20x + 100  =   -4 • (6x² - 5x - 25) 

Trying to factor by splitting the middle term

 3.2     Factoring  6x² - 5x - 25 

The first term is,  6x²  its coefficient is  6 .
The middle term is,  -5x  its coefficient is  -5 .
The last term, "the constant", is  -25 

Step-1 : Multiply the coefficient of the first term by the constant   6 • -25 = -150 

Step-2 : Find two factors of  -150  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,  -15  and  10 
                     6x² - 15x + 10x - 25

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

Final result :

  -4 • (2x - 5) • (3x + 5)