x^4-33*x^2=0

Solution for x^4-33*x^2=0 equation:

Simplifying
x4 + -33x2 = 0

Reorder the terms:
-33x2 + x4 = 0

Solving
-33x2 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-33 + x2) = 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 '(-33 + x2)' equal to zero and attempt to solve:

Simplifying
-33 + x2 = 0

Solving
-33 + x2 = 0

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

Add '33' to each side of the equation.
-33 + 33 + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + x2 = 0 + 33
x2 = 0 + 33

Combine like terms: 0 + 33 = 33
x2 = 33

Simplifying
x2 = 33

Take the square root of each side:
x = {-5.744562647, 5.744562647}
Solution
x = {0, -5.744562647, 5.744562647}