Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  z²-4z-12 

The first term is,  z²  its coefficient is  1 .
The middle term is,  -4z  its coefficient is  -4 .
The last term, "the constant", is  -12 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -12 = -12 

Step-2 : Find two factors of  -12  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,  -6  and  2 
                     z² - 6z + 2z - 12

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

Final result :

  (z + 2) • (z - 6)