Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•32w2) -  w) -  39

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  18w²-w-39 

The first term is,  18w²  its coefficient is  18 .
The middle term is,  -w  its coefficient is  -1 .
The last term, "the constant", is  -39 

Step-1 : Multiply the coefficient of the first term by the constant   18 • -39 = -702 

Step-2 : Find two factors of  -702  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,  -27  and  26 
                     18w² - 27w + 26w - 39

Step-4 : Add up the first 2 terms, pulling out like factors :
                    9w • (2w-3)
              Add up the last 2 terms, pulling out common factors :
                    13 • (2w-3)
Step-5 : Add up the four terms of step 4 :
                    (9w+13)  •  (2w-3)
             Which is the desired factorization

Final result :

  (2w - 3) • (9w + 13)