-6a^5+6a-2a^3=0

Solution for -6a^5+6a-2a^3=0 equation:

Simplifying
-6a5 + 6a + -2a3 = 0

Reorder the terms:
6a + -2a3 + -6a5 = 0

Solving
6a + -2a3 + -6a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(3 + -1a2 + -3a4) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(3 + -1a2 + -3a4)' equal to zero and attempt to solve:

Simplifying
3 + -1a2 + -3a4 = 0

Solving
3 + -1a2 + -3a4 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1 + 0.3333333333a2 + a4 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.3333333333a2 + 1 + a4 = 0 + 1

Reorder the terms:
-1 + 1 + 0.3333333333a2 + a4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.3333333333a2 + a4 = 0 + 1
0.3333333333a2 + a4 = 0 + 1

Combine like terms: 0 + 1 = 1
0.3333333333a2 + a4 = 1

The a term is 0.3333333333a2.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333a2 + 0.02777777779 + a4 = 1 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333a2 + a4 = 1 + 0.02777777779

Combine like terms: 1 + 0.02777777779 = 1.02777777779
0.02777777779 + 0.3333333333a2 + a4 = 1.02777777779

Factor a perfect square on the left side:
(a2 + 0.1666666667)(a2 + 0.1666666667) = 1.02777777779

Calculate the square root of the right side: 1.013793755

Break this problem into two subproblems by setting 
(a2 + 0.1666666667) equal to 1.013793755 and -1.013793755.

Subproblem 1
a2 + 0.1666666667 = 1.013793755

Simplifying
a2 + 0.1666666667 = 1.013793755

Reorder the terms:
0.1666666667 + a2 = 1.013793755

Solving
0.1666666667 + a2 = 1.013793755

Solving for variable 'a'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + a2 = 1.013793755 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + a2 = 1.013793755 + -0.1666666667
a2 = 1.013793755 + -0.1666666667

Combine like terms: 1.013793755 + -0.1666666667 = 0.8471270883
a2 = 0.8471270883

Simplifying
a2 = 0.8471270883

Take the square root of each side:
a = {-0.920395072, 0.920395072}

Subproblem 2
a2 + 0.1666666667 = -1.013793755

Simplifying
a2 + 0.1666666667 = -1.013793755

Reorder the terms:
0.1666666667 + a2 = -1.013793755

Solving
0.1666666667 + a2 = -1.013793755

Solving for variable 'a'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + a2 = -1.013793755 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + a2 = -1.013793755 + -0.1666666667
a2 = -1.013793755 + -0.1666666667

Combine like terms: -1.013793755 + -0.1666666667 = -1.1804604217
a2 = -1.1804604217

Simplifying
a2 = -1.1804604217

Reorder the terms:
1.1804604217 + a2 = -1.1804604217 + 1.1804604217

Combine like terms: -1.1804604217 + 1.1804604217 = 0.0000000000
1.1804604217 + a2 = 0.0000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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