Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•5w2) -  31w) +  15

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  10w²-31w+15 

The first term is,  10w²  its coefficient is  10 .
The middle term is,  -31w  its coefficient is  -31 .
The last term, "the constant", is  +15 

Step-1 : Multiply the coefficient of the first term by the constant   10 • 15 = 150 

Step-2 : Find two factors of  150  whose sum equals the coefficient of the middle term, which is   -31 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -25  and  -6 
                     10w² - 25w - 6w - 15

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

Final result :

  (2w - 5) • (5w - 3)