Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5x2 -  24x) -  5

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5x²-24x-5 

The first term is,  5x²  its coefficient is  5 .
The middle term is,  -24x  its coefficient is  -24 .
The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -5 = -25 

Step-2 : Find two factors of  -25  whose sum equals the coefficient of the middle term, which is   -24 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -25  and  1 
                     5x² - 25x + 1x - 5

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

Final result :

  (x - 5) • (5x + 1)