14z^5-42z^4+6z^3=

Solution for 14z^5-42z^4+6z^3= equation:

Simplifying
14z5 + -42z4 + 6z3 = 0

Reorder the terms:
6z3 + -42z4 + 14z5 = 0

Solving
6z3 + -42z4 + 14z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2z3'.
2z3(3 + -21z + 7z2) = 0

Ignore the factor 2.
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 '(3 + -21z + 7z2)' equal to zero and attempt to solve:

Simplifying
3 + -21z + 7z2 = 0

Solving
3 + -21z + 7z2 = 0

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

Divide each side by '7'.
0.4285714286 + -3z + z2 = 0

Move the constant term to the right:

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -3z + -0.4285714286 + z2 = 0 + -0.4285714286

Reorder the terms:
0.4285714286 + -0.4285714286 + -3z + z2 = 0 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + -3z + z2 = 0 + -0.4285714286
-3z + z2 = 0 + -0.4285714286

Combine like terms: 0 + -0.4285714286 = -0.4285714286
-3z + z2 = -0.4285714286

The z term is -3z.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3z + 2.25 + z2 = -0.4285714286 + 2.25

Reorder the terms:
2.25 + -3z + z2 = -0.4285714286 + 2.25

Combine like terms: -0.4285714286 + 2.25 = 1.8214285714
2.25 + -3z + z2 = 1.8214285714

Factor a perfect square on the left side:
(z + -1.5)(z + -1.5) = 1.8214285714

Calculate the square root of the right side: 1.349603116

Break this problem into two subproblems by setting 
(z + -1.5) equal to 1.349603116 and -1.349603116.

Subproblem 1
z + -1.5 = 1.349603116

Simplifying
z + -1.5 = 1.349603116

Reorder the terms:
-1.5 + z = 1.349603116

Solving
-1.5 + z = 1.349603116

Solving for variable 'z'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + z = 1.349603116 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + z = 1.349603116 + 1.5
z = 1.349603116 + 1.5

Combine like terms: 1.349603116 + 1.5 = 2.849603116
z = 2.849603116

Simplifying
z = 2.849603116

Subproblem 2
z + -1.5 = -1.349603116

Simplifying
z + -1.5 = -1.349603116

Reorder the terms:
-1.5 + z = -1.349603116

Solving
-1.5 + z = -1.349603116

Solving for variable 'z'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + z = -1.349603116 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + z = -1.349603116 + 1.5
z = -1.349603116 + 1.5

Combine like terms: -1.349603116 + 1.5 = 0.150396884
z = 0.150396884

Simplifying
z = 0.150396884

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {2.849603116, 0.150396884}
Solution
z = {2.849603116, 0.150396884}