Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3g2 -  7g) +  2

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3g²-7g+2 

The first term is,  3g²  its coefficient is  3 .
The middle term is,  -7g  its coefficient is  -7 .
The last term, "the constant", is  +2 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 2 = 6 

Step-2 : Find two factors of  6  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,  -6  and  -1 
                     3g² - 6g - 1g - 2

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

Final result :

  (g - 2) • (3g - 1)