Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  (2•7z2)) +  70z) +  336

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -14z² + 70z + 336  =   -14 • (z² - 5z - 24) 

Trying to factor by splitting the middle term

 3.2     Factoring  z² - 5z - 24 

The first term is,  z²  its coefficient is  1 .
The middle term is,  -5z  its coefficient is  -5 .
The last term, "the constant", is  -24 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -24 = -24 

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3 
                     z² - 8z + 3z - 24

Step-4 : Add up the first 2 terms, pulling out like factors :
                    z • (z-8)
              Add up the last 2 terms, pulling out common factors :
                    3 • (z-8)
Step-5 : Add up the four terms of step 4 :
                    (z+3)  •  (z-8)
             Which is the desired factorization

Final result :

  -14 • (z + 3) • (z - 8)