Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•32v2) -  15v) -  18

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   18v² - 15v - 18  =   3 • (6v² - 5v - 6) 

Trying to factor by splitting the middle term

 3.2     Factoring  6v² - 5v - 6 

The first term is,  6v²  its coefficient is  6 .
The middle term is,  -5v  its coefficient is  -5 .
The last term, "the constant", is  -6 

Step-1 : Multiply the coefficient of the first term by the constant   6 • -6 = -36 

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  4 
                     6v² - 9v + 4v - 6

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

Final result :

  3 • (2v - 3) • (3v + 2)