Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3z2 +  11z) -  14

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3z²+11z-14 

The first term is,  3z²  its coefficient is  3 .
The middle term is,  +11z  its coefficient is  11 .
The last term, "the constant", is  -14 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -14 = -42 

Step-2 : Find two factors of  -42  whose sum equals the coefficient of the middle term, which is   11 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  14 
                     3z² - 3z + 14z - 14

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3z • (z-1)
              Add up the last 2 terms, pulling out common factors :
                    14 • (z-1)
Step-5 : Add up the four terms of step 4 :
                    (3z+14)  •  (z-1)
             Which is the desired factorization

Final result :

  (z - 1) • (3z + 14)