Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3f2 +  2f) -  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3f²+2f-1 

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

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

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   2 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  3 
                     3f² - 1f + 3f - 1

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

Final result :

  (3f - 1) • (f + 1)