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

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


Simplifying
0 = (x + -1i)(x + i)(x + -2i)(x + 2i)

Reorder the terms:
0 = (-1i + x)(x + i)(x + -2i)(x + 2i)

Reorder the terms:
0 = (-1i + x)(i + x)(x + -2i)(x + 2i)

Reorder the terms:
0 = (-1i + x)(i + x)(-2i + x)(x + 2i)

Reorder the terms:
0 = (-1i + x)(i + x)(-2i + x)(2i + x)

Multiply (-1i + x) * (i + x)
0 = (-1i * (i + x) + x(i + x))(-2i + x)(2i + x)
0 = ((i * -1i + x * -1i) + x(i + x))(-2i + x)(2i + x)

Reorder the terms:
0 = ((-1ix + -1i2) + x(i + x))(-2i + x)(2i + x)
0 = ((-1ix + -1i2) + x(i + x))(-2i + x)(2i + x)
0 = (-1ix + -1i2 + (i * x + x * x))(-2i + x)(2i + x)
0 = (-1ix + -1i2 + (ix + x2))(-2i + x)(2i + x)

Reorder the terms:
0 = (-1ix + ix + -1i2 + x2)(-2i + x)(2i + x)

Combine like terms: -1ix + ix = 0
0 = (0 + -1i2 + x2)(-2i + x)(2i + x)
0 = (-1i2 + x2)(-2i + x)(2i + x)

Multiply (-1i2 + x2) * (-2i + x)
0 = (-1i2 * (-2i + x) + x2(-2i + x))(2i + x)
0 = ((-2i * -1i2 + x * -1i2) + x2(-2i + x))(2i + x)

Reorder the terms:
0 = ((-1i2x + 2i3) + x2(-2i + x))(2i + x)
0 = ((-1i2x + 2i3) + x2(-2i + x))(2i + x)
0 = (-1i2x + 2i3 + (-2i * x2 + x * x2))(2i + x)
0 = (-1i2x + 2i3 + (-2ix2 + x3))(2i + x)

Reorder the terms:
0 = (-2ix2 + -1i2x + 2i3 + x3)(2i + x)
0 = (-2ix2 + -1i2x + 2i3 + x3)(2i + x)

Multiply (-2ix2 + -1i2x + 2i3 + x3) * (2i + x)
0 = (-2ix2 * (2i + x) + -1i2x * (2i + x) + 2i3 * (2i + x) + x3(2i + x))
0 = ((2i * -2ix2 + x * -2ix2) + -1i2x * (2i + x) + 2i3 * (2i + x) + x3(2i + x))

Reorder the terms:
0 = ((-2ix3 + -4i2x2) + -1i2x * (2i + x) + 2i3 * (2i + x) + x3(2i + x))
0 = ((-2ix3 + -4i2x2) + -1i2x * (2i + x) + 2i3 * (2i + x) + x3(2i + x))
0 = (-2ix3 + -4i2x2 + (2i * -1i2x + x * -1i2x) + 2i3 * (2i + x) + x3(2i + x))

Reorder the terms:
0 = (-2ix3 + -4i2x2 + (-1i2x2 + -2i3x) + 2i3 * (2i + x) + x3(2i + x))
0 = (-2ix3 + -4i2x2 + (-1i2x2 + -2i3x) + 2i3 * (2i + x) + x3(2i + x))
0 = (-2ix3 + -4i2x2 + -1i2x2 + -2i3x + (2i * 2i3 + x * 2i3) + x3(2i + x))

Reorder the terms:
0 = (-2ix3 + -4i2x2 + -1i2x2 + -2i3x + (2i3x + 4i4) + x3(2i + x))
0 = (-2ix3 + -4i2x2 + -1i2x2 + -2i3x + (2i3x + 4i4) + x3(2i + x))
0 = (-2ix3 + -4i2x2 + -1i2x2 + -2i3x + 2i3x + 4i4 + (2i * x3 + x * x3))
0 = (-2ix3 + -4i2x2 + -1i2x2 + -2i3x + 2i3x + 4i4 + (2ix3 + x4))

Reorder the terms:
0 = (-2ix3 + 2ix3 + -4i2x2 + -1i2x2 + -2i3x + 2i3x + 4i4 + x4)

Combine like terms: -2ix3 + 2ix3 = 0
0 = (0 + -4i2x2 + -1i2x2 + -2i3x + 2i3x + 4i4 + x4)
0 = (-4i2x2 + -1i2x2 + -2i3x + 2i3x + 4i4 + x4)

Combine like terms: -4i2x2 + -1i2x2 = -5i2x2
0 = (-5i2x2 + -2i3x + 2i3x + 4i4 + x4)

Combine like terms: -2i3x + 2i3x = 0
0 = (-5i2x2 + 0 + 4i4 + x4)
0 = (-5i2x2 + 4i4 + x4)

Solving
0 = -5i2x2 + 4i4 + x4

Solving for variable 'i'.
Remove the zero:
5i2x2 + -4i4 + -1x4 = -5i2x2 + 4i4 + x4 + 5i2x2 + -4i4 + -1x4

Reorder the terms:
5i2x2 + -4i4 + -1x4 = -5i2x2 + 5i2x2 + 4i4 + -4i4 + x4 + -1x4

Combine like terms: -5i2x2 + 5i2x2 = 0
5i2x2 + -4i4 + -1x4 = 0 + 4i4 + -4i4 + x4 + -1x4
5i2x2 + -4i4 + -1x4 = 4i4 + -4i4 + x4 + -1x4

Combine like terms: 4i4 + -4i4 = 0
5i2x2 + -4i4 + -1x4 = 0 + x4 + -1x4
5i2x2 + -4i4 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
5i2x2 + -4i4 + -1x4 = 0

Factor a trinomial.
(-4i2 + x2)(i2 + -1x2) = 0

Factor a difference between two squares.
((2i + x)(-2i + x))(i2 + -1x2) = 0

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


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

Simplifying
2i + x = 0

Solving
2i + x = 0

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

Add '-1x' to each side of the equation.
2i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
2i + 0 = 0 + -1x
2i = 0 + -1x
Remove the zero:
2i = -1x

Divide each side by '2'.
i = -0.5x

Simplifying
i = -0.5x

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

Simplifying
-2i + x = 0

Solving
-2i + x = 0

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

Add '-1x' to each side of the equation.
-2i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
-2i + 0 = 0 + -1x
-2i = 0 + -1x
Remove the zero:
-2i = -1x

Divide each side by '-2'.
i = 0.5x

Simplifying
i = 0.5x

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

Simplifying
i + x = 0

Solving
i + x = 0

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

Add '-1x' to each side of the equation.
i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
i + 0 = 0 + -1x
i = 0 + -1x
Remove the zero:
i = -1x

Simplifying
i = -1x

Subproblem 4
Set the factor '(i + -1x)' equal to zero and attempt to solve:

Simplifying
i + -1x = 0

Solving
i + -1x = 0

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

Add 'x' to each side of the equation.
i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
i + 0 = 0 + x
i = 0 + x
Remove the zero:
i = x

Simplifying
i = x
Solution
i = {-0.5x, 0.5x, -1x, x}

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