x^2(x^2+2)(x^2-2)=0

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Solution for x^2(x^2+2)(x^2-2)=0 equation: 


Simplifying
x2(x2 + 2)(x2 + -2) = 0

Reorder the terms:
x2(2 + x2)(x2 + -2) = 0

Reorder the terms:
x2(2 + x2)(-2 + x2) = 0

Multiply (2 + x2) * (-2 + x2)
x2(2(-2 + x2) + x2(-2 + x2)) = 0
x2((-2 * 2 + x2 * 2) + x2(-2 + x2)) = 0
x2((-4 + 2x2) + x2(-2 + x2)) = 0
x2(-4 + 2x2 + (-2 * x2 + x2 * x2)) = 0
x2(-4 + 2x2 + (-2x2 + x4)) = 0

Combine like terms: 2x2 + -2x2 = 0
x2(-4 + 0 + x4) = 0
x2(-4 + x4) = 0
(-4 * x2 + x4 * x2) = 0
(-4x2 + x6) = 0

Solving
-4x2 + x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-4 + x4) = 0

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

Simplifying
2 + x2 = 0

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

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

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

Simplifying
x2 = -2

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 '(-2 + x2)' equal to zero and attempt to solve:

Simplifying
-2 + x2 = 0

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

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

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

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {0, -1.414213562, 1.414213562}

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