Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•3w2) -  28w) +  16

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   6w² - 28w + 16  =   2 • (3w² - 14w + 8) 

Trying to factor by splitting the middle term

 3.2     Factoring  3w² - 14w + 8 

The first term is,  3w²  its coefficient is  3 .
The middle term is,  -14w  its coefficient is  -14 .
The last term, "the constant", is  +8 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 8 = 24 

Step-2 : Find two factors of  24  whose sum equals the coefficient of the middle term, which is   -14 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  -2 
                     3w² - 12w - 2w - 8

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

Final result :

  2 • (w - 4) • (3w - 2)