14z^4+10z^3+4z^2=

Solution for 14z^4+10z^3+4z^2= equation:

Simplifying
14z4 + 10z3 + 4z2 = 0

Reorder the terms:
4z2 + 10z3 + 14z4 = 0

Solving
4z2 + 10z3 + 14z4 = 0

Solving for variable 'z'.

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

Ignore the factor 2.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(2 + 5z + 7z2)' equal to zero and attempt to solve:

Simplifying
2 + 5z + 7z2 = 0

Solving
2 + 5z + 7z2 = 0

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

Divide each side by '7'.
0.2857142857 + 0.7142857143z + z2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + 0.7142857143z + -0.2857142857 + z2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + 0.7142857143z + z2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + 0.7142857143z + z2 = 0 + -0.2857142857
0.7142857143z + z2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
0.7142857143z + z2 = -0.2857142857

The z term is 0.7142857143z.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143z + 0.1275510204 + z2 = -0.2857142857 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143z + z2 = -0.2857142857 + 0.1275510204

Combine like terms: -0.2857142857 + 0.1275510204 = -0.1581632653
0.1275510204 + 0.7142857143z + z2 = -0.1581632653

Factor a perfect square on the left side:
(z + 0.3571428572)(z + 0.3571428572) = -0.1581632653

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}