Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•5w2) -  19w) -  15

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  10w²-19w-15 

The first term is,  10w²  its coefficient is  10 .
The middle term is,  -19w  its coefficient is  -19 .
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   -19 .

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)