x^4-32x^2=32x^2

Solution for x^4-32x^2=32x^2 equation:

Simplifying
x4 + -32x2 = 32x2

Reorder the terms:
-32x2 + x4 = 32x2

Solving
-32x2 + x4 = 32x2

Solving for variable 'x'.

Reorder the terms:
-32x2 + -32x2 + x4 = 32x2 + -32x2

Combine like terms: -32x2 + -32x2 = -64x2
-64x2 + x4 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
-64x2 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-64 + x2) = 0

Factor a difference between two squares.
x2((8 + x)(-8 + x)) = 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 '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Subproblem 3
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Solution
x = {0, -8, 8}