0=25x^4-6x^2

Solution for 0=25x^4-6x^2 equation:

Simplifying
0 = 25x4 + -6x2

Reorder the terms:
0 = -6x2 + 25x4

Solving
0 = -6x2 + 25x4

Solving for variable 'x'.
Remove the zero:
6x2 + -25x4 = -6x2 + 25x4 + 6x2 + -25x4

Reorder the terms:
6x2 + -25x4 = -6x2 + 6x2 + 25x4 + -25x4

Combine like terms: -6x2 + 6x2 = 0
6x2 + -25x4 = 0 + 25x4 + -25x4
6x2 + -25x4 = 25x4 + -25x4

Combine like terms: 25x4 + -25x4 = 0
6x2 + -25x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(6 + -25x2) = 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 '(6 + -25x2)' equal to zero and attempt to solve:

Simplifying
6 + -25x2 = 0

Solving
6 + -25x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -25x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -25x2 = 0 + -6
-25x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-25x2 = -6

Divide each side by '-25'.
x2 = 0.24

Simplifying
x2 = 0.24

Take the square root of each side:
x = {-0.489897949, 0.489897949}
Solution
x = {0, -0.489897949, 0.489897949}