Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3w2 -  7w) -  66

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3w²-7w-66 

The first term is,  3w²  its coefficient is  3 .
The middle term is,  -7w  its coefficient is  -7 .
The last term, "the constant", is  -66 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -66 = -198 

Step-2 : Find two factors of  -198  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  11 
                     3w² - 18w + 11w - 66

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3w • (w-6)
              Add up the last 2 terms, pulling out common factors :
                    11 • (w-6)
Step-5 : Add up the four terms of step 4 :
                    (3w+11)  •  (w-6)
             Which is the desired factorization

Final result :

  (w - 6) • (3w + 11)