Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2w2 +  5w) -  63

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2w²+5w-63 

The first term is,  2w²  its coefficient is  2 .
The middle term is,  +5w  its coefficient is  5 .
The last term, "the constant", is  -63 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -63 = -126 

Step-2 : Find two factors of  -126  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  14 
                     2w² - 9w + 14w - 63

Step-4 : Add up the first 2 terms, pulling out like factors :
                    w • (2w-9)
              Add up the last 2 terms, pulling out common factors :
                    7 • (2w-9)
Step-5 : Add up the four terms of step 4 :
                    (w+7)  •  (2w-9)
             Which is the desired factorization

Final result :

  (2w - 9) • (w + 7)