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

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

Simplifying
3x4 + 2x2 = 5x6

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

Solving
2x2 + 3x4 = 5x6

Solving for variable 'x'.

Combine like terms: 5x6 + -5x6 = 0
2x2 + 3x4 + -5x6 = 0

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

Factor a trinomial.
x2((1 + -1x2)(2 + 5x2)) = 0

Factor a difference between two squares.
x2(((1 + x)(1 + -1x))(2 + 5x2)) = 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 + 5x2)' equal to zero and attempt to solve:

Simplifying
2 + 5x2 = 0

Solving
2 + 5x2 = 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 + 5x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x2 = 0 + -2
5x2 = 0 + -2

Combine like terms: 0 + -2 = -2
5x2 = -2

Divide each side by '5'.
x2 = -0.4

Simplifying
x2 = -0.4

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 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 4
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, -1, 1}