Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•3v2) -  26v) -  56

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   12v² - 26v - 56  =   2 • (6v² - 13v - 28) 

Trying to factor by splitting the middle term

 3.2     Factoring  6v² - 13v - 28 

The first term is,  6v²  its coefficient is  6 .
The middle term is,  -13v  its coefficient is  -13 .
The last term, "the constant", is  -28 

Step-1 : Multiply the coefficient of the first term by the constant   6 • -28 = -168 

Step-2 : Find two factors of  -168  whose sum equals the coefficient of the middle term, which is   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -21  and  8 
                     6v² - 21v + 8v - 28

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

Final result :

  2 • (2v - 7) • (3v + 4)