Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (24b2 +  60b) -  100

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   16b² + 60b - 100  =   4 • (4b² + 15b - 25) 

Trying to factor by splitting the middle term

 3.2     Factoring  4b² + 15b - 25 

The first term is,  4b²  its coefficient is  4 .
The middle term is,  +15b  its coefficient is  15 .
The last term, "the constant", is  -25 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -25 = -100 

Step-2 : Find two factors of  -100  whose sum equals the coefficient of the middle term, which is   15 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  20 
                     4b² - 5b + 20b - 25

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

Final result :

  4 • (4b - 5) • (b + 5)