Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22z2 -  34z) -  38

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4z² - 34z - 38  =   2 • (2z² - 17z - 19) 

Trying to factor by splitting the middle term

 3.2     Factoring  2z² - 17z - 19 

The first term is,  2z²  its coefficient is  2 .
The middle term is,  -17z  its coefficient is  -17 .
The last term, "the constant", is  -19 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -19 = -38 

Step-2 : Find two factors of  -38  whose sum equals the coefficient of the middle term, which is   -17 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -19  and  2 
                     2z² - 19z + 2z - 19

Step-4 : Add up the first 2 terms, pulling out like factors :
                    z • (2z-19)
              Add up the last 2 terms, pulling out common factors :
                     1 • (2z-19)
Step-5 : Add up the four terms of step 4 :
                    (z+1)  •  (2z-19)
             Which is the desired factorization

Final result :

  2 • (2z - 19) • (z + 1)