Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2x2 -  8x) +  6

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2x² - 8x + 6  =   2 • (x² - 4x + 3) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - 4x + 3 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -4x  its coefficient is  -4 .
The last term, "the constant", is  +3 

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

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

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  -1 
                     x² - 3x - 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-3)
              Add up the last 2 terms, pulling out common factors :
                     1 • (x-3)
Step-5 : Add up the four terms of step 4 :
                    (x-1)  •  (x-3)
             Which is the desired factorization

Final result :

  2 • (x - 1) • (x - 3)