Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2w2 -  9w) +  4

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2w²-9w+4 

The first term is,  2w²  its coefficient is  2 .
The middle term is,  -9w  its coefficient is  -9 .
The last term, "the constant", is  +4 

Step-1 : Multiply the coefficient of the first term by the constant   2 • 4 = 8 

Step-2 : Find two factors of  8  whose sum equals the coefficient of the middle term, which is   -9 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  -1 
                     2w² - 8w - 1w - 4

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2w • (w-4)
              Add up the last 2 terms, pulling out common factors :
                     1 • (w-4)
Step-5 : Add up the four terms of step 4 :
                    (2w-1)  •  (w-4)
             Which is the desired factorization

Final result :

  (w - 4) • (2w - 1)