Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2w2 +  13w) +  15

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2w²+13w+15 

The first term is,  2w²  its coefficient is  2 .
The middle term is,  +13w  its coefficient is  13 .
The last term, "the constant", is  +15 

Step-1 : Multiply the coefficient of the first term by the constant   2 • 15 = 30 

Step-2 : Find two factors of  30  whose sum equals the coefficient of the middle term, which is   13 .

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

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

Final result :

  (2w + 3) • (w + 5)