Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3w2) -  3w) -  18

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6w² - 3w - 18  =   3 • (2w² - w - 6) 

Trying to factor by splitting the middle term

 3.2     Factoring  2w² - w - 6 

The first term is,  2w²  its coefficient is  2 .
The middle term is,  -w  its coefficient is  -1 .
The last term, "the constant", is  -6 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -6 = -12 

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   -1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  3 
                     2w² - 4w + 3w - 6

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

Final result :

  3 • (w - 2) • (2w + 3)