35z^5-70z^4+14z^3=

Solution for 35z^5-70z^4+14z^3= equation:

Simplifying
35z5 + -70z4 + 14z3 = 0

Reorder the terms:
14z3 + -70z4 + 35z5 = 0

Solving
14z3 + -70z4 + 35z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '7z3'.
7z3(2 + -10z + 5z2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'z3' equal to zero and attempt to solve:

Simplifying
z3 = 0

Solving
z3 = 0

Move all terms containing z to the left, all other terms to the right.

Simplifying
z3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2 + -10z + 5z2)' equal to zero and attempt to solve:

Simplifying
2 + -10z + 5z2 = 0

Solving
2 + -10z + 5z2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.4 + -2z + z2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2z + -0.4 + z2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2z + z2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2z + z2 = 0 + -0.4
-2z + z2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2z + z2 = -0.4

The z term is -2z.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z + 1 + z2 = -0.4 + 1

Reorder the terms:
1 + -2z + z2 = -0.4 + 1

Combine like terms: -0.4 + 1 = 0.6
1 + -2z + z2 = 0.6

Factor a perfect square on the left side:
(z + -1)(z + -1) = 0.6

Calculate the square root of the right side: 0.774596669

Break this problem into two subproblems by setting 
(z + -1) equal to 0.774596669 and -0.774596669.

Subproblem 1
z + -1 = 0.774596669

Simplifying
z + -1 = 0.774596669

Reorder the terms:
-1 + z = 0.774596669

Solving
-1 + z = 0.774596669

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + z = 0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + z = 0.774596669 + 1
z = 0.774596669 + 1

Combine like terms: 0.774596669 + 1 = 1.774596669
z = 1.774596669

Simplifying
z = 1.774596669

Subproblem 2
z + -1 = -0.774596669

Simplifying
z + -1 = -0.774596669

Reorder the terms:
-1 + z = -0.774596669

Solving
-1 + z = -0.774596669

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + z = -0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + z = -0.774596669 + 1
z = -0.774596669 + 1

Combine like terms: -0.774596669 + 1 = 0.225403331
z = 0.225403331

Simplifying
z = 0.225403331

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.774596669, 0.225403331}
Solution
z = {1.774596669, 0.225403331}