Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  w²-15w+54 

The first term is,  w²  its coefficient is  1 .
The middle term is,  -15w  its coefficient is  -15 .
The last term, "the constant", is  +54 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 54 = 54 

Step-2 : Find two factors of  54  whose sum equals the coefficient of the middle term, which is   -15 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -6 
                     w² - 9w - 6w - 54

Step-4 : Add up the first 2 terms, pulling out like factors :
                    w • (w-9)
              Add up the last 2 terms, pulling out common factors :
                    6 • (w-9)
Step-5 : Add up the four terms of step 4 :
                    (w-6)  •  (w-9)
             Which is the desired factorization

Final result :

  (w - 6) • (w - 9)