2x^4-5x^2=0

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

Simplifying
2x4 + -5x2 = 0

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

Solving
-5x2 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-5 + 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 '(-5 + 2x2)' equal to zero and attempt to solve:

Simplifying
-5 + 2x2 = 0

Solving
-5 + 2x2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x2 = 0 + 5

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

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

Divide each side by '2'.
x2 = 2.5

Simplifying
x2 = 2.5

Take the square root of each side:
x = {-1.58113883, 1.58113883}
Solution
x = {0, -1.58113883, 1.58113883}