Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((24•5x2) -  4x) -  4

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   80x² - 4x - 4  =   4 • (20x² - x - 1) 

Trying to factor by splitting the middle term

 3.2     Factoring  20x² - x - 1 

The first term is,  20x²  its coefficient is  20 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  -1 

Step-1 : Multiply the coefficient of the first term by the constant   20 • -1 = -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 
                     20x² - 5x + 4x - 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    5x • (4x-1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (4x-1)
Step-5 : Add up the four terms of step 4 :
                    (5x+1)  •  (4x-1)
             Which is the desired factorization

Final result :

  4 • (4x - 1) • (5x + 1)