(x^2-2)(x^2+2)(x^2+4)(x+2)(x-2)=0

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Solution for (x^2-2)(x^2+2)(x^2+4)(x+2)(x-2)=0 equation:


Simplifying
(x2 + -2)(x2 + 2)(x2 + 4)(x + 2)(x + -2) = 0

Reorder the terms:
(-2 + x2)(x2 + 2)(x2 + 4)(x + 2)(x + -2) = 0

Reorder the terms:
(-2 + x2)(2 + x2)(x2 + 4)(x + 2)(x + -2) = 0

Reorder the terms:
(-2 + x2)(2 + x2)(4 + x2)(x + 2)(x + -2) = 0

Reorder the terms:
(-2 + x2)(2 + x2)(4 + x2)(2 + x)(x + -2) = 0

Reorder the terms:
(-2 + x2)(2 + x2)(4 + x2)(2 + x)(-2 + x) = 0

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

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

Multiply (-4 + x4) * (4 + x2)
(-4(4 + x2) + x4(4 + x2))(2 + x)(-2 + x) = 0
((4 * -4 + x2 * -4) + x4(4 + x2))(2 + x)(-2 + x) = 0
((-16 + -4x2) + x4(4 + x2))(2 + x)(-2 + x) = 0
(-16 + -4x2 + (4 * x4 + x2 * x4))(2 + x)(-2 + x) = 0
(-16 + -4x2 + (4x4 + x6))(2 + x)(-2 + x) = 0
(-16 + -4x2 + 4x4 + x6)(2 + x)(-2 + x) = 0

Multiply (-16 + -4x2 + 4x4 + x6) * (2 + x)
(-16(2 + x) + -4x2 * (2 + x) + 4x4 * (2 + x) + x6(2 + x))(-2 + x) = 0
((2 * -16 + x * -16) + -4x2 * (2 + x) + 4x4 * (2 + x) + x6(2 + x))(-2 + x) = 0
((-32 + -16x) + -4x2 * (2 + x) + 4x4 * (2 + x) + x6(2 + x))(-2 + x) = 0
(-32 + -16x + (2 * -4x2 + x * -4x2) + 4x4 * (2 + x) + x6(2 + x))(-2 + x) = 0
(-32 + -16x + (-8x2 + -4x3) + 4x4 * (2 + x) + x6(2 + x))(-2 + x) = 0
(-32 + -16x + -8x2 + -4x3 + (2 * 4x4 + x * 4x4) + x6(2 + x))(-2 + x) = 0
(-32 + -16x + -8x2 + -4x3 + (8x4 + 4x5) + x6(2 + x))(-2 + x) = 0
(-32 + -16x + -8x2 + -4x3 + 8x4 + 4x5 + (2 * x6 + x * x6))(-2 + x) = 0
(-32 + -16x + -8x2 + -4x3 + 8x4 + 4x5 + (2x6 + x7))(-2 + x) = 0
(-32 + -16x + -8x2 + -4x3 + 8x4 + 4x5 + 2x6 + x7)(-2 + x) = 0

Multiply (-32 + -16x + -8x2 + -4x3 + 8x4 + 4x5 + 2x6 + x7) * (-2 + x)
(-32(-2 + x) + -16x * (-2 + x) + -8x2 * (-2 + x) + -4x3 * (-2 + x) + 8x4 * (-2 + x) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
((-2 * -32 + x * -32) + -16x * (-2 + x) + -8x2 * (-2 + x) + -4x3 * (-2 + x) + 8x4 * (-2 + x) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
((64 + -32x) + -16x * (-2 + x) + -8x2 * (-2 + x) + -4x3 * (-2 + x) + 8x4 * (-2 + x) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + (-2 * -16x + x * -16x) + -8x2 * (-2 + x) + -4x3 * (-2 + x) + 8x4 * (-2 + x) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + (32x + -16x2) + -8x2 * (-2 + x) + -4x3 * (-2 + x) + 8x4 * (-2 + x) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + (-2 * -8x2 + x * -8x2) + -4x3 * (-2 + x) + 8x4 * (-2 + x) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + (16x2 + -8x3) + -4x3 * (-2 + x) + 8x4 * (-2 + x) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + (-2 * -4x3 + x * -4x3) + 8x4 * (-2 + x) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + (8x3 + -4x4) + 8x4 * (-2 + x) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + (-2 * 8x4 + x * 8x4) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + (-16x4 + 8x5) + 4x5 * (-2 + x) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + (-2 * 4x5 + x * 4x5) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + (-8x5 + 4x6) + 2x6 * (-2 + x) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + (-2 * 2x6 + x * 2x6) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + (-4x6 + 2x7) + x7(-2 + x)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + -4x6 + 2x7 + (-2 * x7 + x * x7)) = 0
(64 + -32x + 32x + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + -4x6 + 2x7 + (-2x7 + x8)) = 0

Combine like terms: -32x + 32x = 0
(64 + 0 + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + -4x6 + 2x7 + -2x7 + x8) = 0
(64 + -16x2 + 16x2 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + -4x6 + 2x7 + -2x7 + x8) = 0

Combine like terms: -16x2 + 16x2 = 0
(64 + 0 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + -4x6 + 2x7 + -2x7 + x8) = 0
(64 + -8x3 + 8x3 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + -4x6 + 2x7 + -2x7 + x8) = 0

Combine like terms: -8x3 + 8x3 = 0
(64 + 0 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + -4x6 + 2x7 + -2x7 + x8) = 0
(64 + -4x4 + -16x4 + 8x5 + -8x5 + 4x6 + -4x6 + 2x7 + -2x7 + x8) = 0

Combine like terms: -4x4 + -16x4 = -20x4
(64 + -20x4 + 8x5 + -8x5 + 4x6 + -4x6 + 2x7 + -2x7 + x8) = 0

Combine like terms: 8x5 + -8x5 = 0
(64 + -20x4 + 0 + 4x6 + -4x6 + 2x7 + -2x7 + x8) = 0
(64 + -20x4 + 4x6 + -4x6 + 2x7 + -2x7 + x8) = 0

Combine like terms: 4x6 + -4x6 = 0
(64 + -20x4 + 0 + 2x7 + -2x7 + x8) = 0
(64 + -20x4 + 2x7 + -2x7 + x8) = 0

Combine like terms: 2x7 + -2x7 = 0
(64 + -20x4 + 0 + x8) = 0
(64 + -20x4 + x8) = 0

Solving
64 + -20x4 + x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x4)(16 + -1x4) = 0

Factor a difference between two squares.
((2 + x2)(2 + -1x2))(16 + -1x4) = 0

Factor a difference between two squares.
((4 + x2)(4 + -1x2))(2 + x2)(2 + -1x2) = 0

Factor a difference between two squares.
((4 + x2)((2 + x)(2 + -1x)))(2 + x2)(2 + -1x2) = 0


Subproblem 1
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 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 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 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

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

Subproblem 3
Set the factor '(4 + x2)' equal to zero and attempt to solve:

Simplifying
4 + x2 = 0

Solving
4 + x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = 0 + -4
x2 = 0 + -4

Combine like terms: 0 + -4 = -4
x2 = -4

Simplifying
x2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 4
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

Subproblem 5
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.414213562, 1.414213562, -2, 2}

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