Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3v2 -  7v) -  20

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3v²-7v-20 

The first term is,  3v²  its coefficient is  3 .
The middle term is,  -7v  its coefficient is  -7 .
The last term, "the constant", is  -20 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -20 = -60 

Step-2 : Find two factors of  -60  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  5 
                     3v² - 12v + 5v - 20

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

Final result :

  (v - 4) • (3v + 5)