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". 

Step  1  :

Equation at the end of step  1  :

  ((2•3•5z2) -  71z) +  35

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  30z²-71z+35 

The first term is,  30z²  its coefficient is  30 .
The middle term is,  -71z  its coefficient is  -71 .
The last term, "the constant", is  +35 

Step-1 : Multiply the coefficient of the first term by the constant   30 • 35 = 1050 

Step-2 : Find two factors of  1050  whose sum equals the coefficient of the middle term, which is   -71 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -50  and  -21 
                     30z² - 50z - 21z - 35

Step-4 : Add up the first 2 terms, pulling out like factors :
                    10z • (3z-5)
              Add up the last 2 terms, pulling out common factors :
                    7 • (3z-5)
Step-5 : Add up the four terms of step 4 :
                    (10z-7)  •  (3z-5)
             Which is the desired factorization

Final result :

  (3z - 5) • (10z - 7)