2x^6+5x^4-3x^2=0

Solution for 2x^6+5x^4-3x^2=0 equation:

Simplifying
2x6 + 5x4 + -3x2 = 0

Reorder the terms:
-3x2 + 5x4 + 2x6 = 0

Solving
-3x2 + 5x4 + 2x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-3 + 5x2 + 2x4) = 0

Factor a trinomial.
x2((-3 + -1x2)(1 + -2x2)) = 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 '(-3 + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + -1x2 = 0

Solving
-3 + -1x2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x2 = 0 + 3
-1x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x2 = 3

Divide each side by '-1'.
x2 = -3

Simplifying
x2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x2 = 0 + -1
-2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x2 = -1

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Solution
x = {0, -0.707106781, 0.707106781}