Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5s2 +  24s) -  5

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  5s²+24s-5 

The first term is,  5s²  its coefficient is  5 .
The middle term is,  +24s  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,  -1  and  25 
                     5s² - 1s + 25s - 5

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

Final result :

  (5s - 1) • (s + 5)