3x^6+2x^2=0

Solution for 3x^6+2x^2=0 equation:

Simplifying
3x6 + 2x2 = 0

Reorder the terms:
2x2 + 3x6 = 0

Solving
2x2 + 3x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(2 + 3x4) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(2 + 3x4)' equal to zero and attempt to solve:

Simplifying
2 + 3x4 = 0

Solving
2 + 3x4 = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x4 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x4 = 0 + -2
3x4 = 0 + -2

Combine like terms: 0 + -2 = -2
3x4 = -2

Divide each side by '3'.
x4 = -0.6666666667

Simplifying
x4 = -0.6666666667

The solution to this equation could not be determined.

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