Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "z2"   was replaced by   "z^2".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  ((3 • (z3)) -  (2•3z2)) -  24z
 Step  2  :

Equation at the end of step  2  :

  (3z3 -  (2•3z2)) -  24z

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   3z³ - 6z² - 24z  =   3z • (z² - 2z - 8) 

Trying to factor by splitting the middle term

 4.2     Factoring  z² - 2z - 8 

The first term is,  z²  its coefficient is  1 .
The middle term is,  -2z  its coefficient is  -2 .
The last term, "the constant", is  -8 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -8 = -8 

Step-2 : Find two factors of  -8  whose sum equals the coefficient of the middle term, which is   -2 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  2 
                     z² - 4z + 2z - 8

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

Final result :

  3z • (z + 2) • (z - 4)