Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3z2 -  7z) -  6

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3z²-7z-6 

The first term is,  3z²  its coefficient is  3 .
The middle term is,  -7z  its coefficient is  -7 .
The last term, "the constant", is  -6 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -6 = -18 

Step-2 : Find two factors of  -18  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,  -9  and  2 
                     3z² - 9z + 2z - 6

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

Final result :

  (z - 3) • (3z + 2)