Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3v2 -  4v) -  7

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3v²-4v-7 

The first term is,  3v²  its coefficient is  3 .
The middle term is,  -4v  its coefficient is  -4 .
The last term, "the constant", is  -7 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -7 = -21 

Step-2 : Find two factors of  -21  whose sum equals the coefficient of the middle term, which is   -4 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  3 
                     3v² - 7v + 3v - 7

Step-4 : Add up the first 2 terms, pulling out like factors :
                    v • (3v-7)
              Add up the last 2 terms, pulling out common factors :
                     1 • (3v-7)
Step-5 : Add up the four terms of step 4 :
                    (v+1)  •  (3v-7)
             Which is the desired factorization

Final result :

  (3v - 7) • (v + 1)