Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((3•5f2) -  5f) -  10

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   15f² - 5f - 10  =   5 • (3f² - f - 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  3f² - f - 2 

The first term is,  3f²  its coefficient is  3 .
The middle term is,  -f  its coefficient is  -1 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -2 = -6 

Step-2 : Find two factors of  -6  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,  -3  and  2 
                     3f² - 3f + 2f - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3f • (f-1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (f-1)
Step-5 : Add up the four terms of step 4 :
                    (3f+2)  •  (f-1)
             Which is the desired factorization

Final result :

  5 • (f - 1) • (3f + 2)