Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (5w2 -  15w) -  20

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   5w² - 15w - 20  =   5 • (w² - 3w - 4) 

Trying to factor by splitting the middle term

 3.2     Factoring  w² - 3w - 4 

The first term is,  w²  its coefficient is  1 .
The middle term is,  -3w  its coefficient is  -3 .
The last term, "the constant", is  -4 

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

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   -3 .

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

Step-4 : Add up the first 2 terms, pulling out like factors :
                    w • (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 :
                    (w+1)  •  (w-4)
             Which is the desired factorization

Final result :

  5 • (w + 1) • (w - 4)