Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (23x2 -  4x) -  40

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   8x² - 4x - 40  =   4 • (2x² - x - 10) 

Trying to factor by splitting the middle term

 3.2     Factoring  2x² - x - 10 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  -10 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -10 = -20 

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   -1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  4 
                     2x² - 5x + 4x - 10

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

Final result :

  4 • (2x - 5) • (x + 2)