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

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


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

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

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

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

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

Multiply (-2i + x) * (2i + x)
(-2i * (2i + x) + x(2i + x))(-4i + x)(4i + x) = 0
((2i * -2i + x * -2i) + x(2i + x))(-4i + x)(4i + x) = 0

Reorder the terms:
((-2ix + -4i2) + x(2i + x))(-4i + x)(4i + x) = 0
((-2ix + -4i2) + x(2i + x))(-4i + x)(4i + x) = 0
(-2ix + -4i2 + (2i * x + x * x))(-4i + x)(4i + x) = 0
(-2ix + -4i2 + (2ix + x2))(-4i + x)(4i + x) = 0

Reorder the terms:
(-2ix + 2ix + -4i2 + x2)(-4i + x)(4i + x) = 0

Combine like terms: -2ix + 2ix = 0
(0 + -4i2 + x2)(-4i + x)(4i + x) = 0
(-4i2 + x2)(-4i + x)(4i + x) = 0

Multiply (-4i2 + x2) * (-4i + x)
(-4i2 * (-4i + x) + x2(-4i + x))(4i + x) = 0
((-4i * -4i2 + x * -4i2) + x2(-4i + x))(4i + x) = 0

Reorder the terms:
((-4i2x + 16i3) + x2(-4i + x))(4i + x) = 0
((-4i2x + 16i3) + x2(-4i + x))(4i + x) = 0
(-4i2x + 16i3 + (-4i * x2 + x * x2))(4i + x) = 0
(-4i2x + 16i3 + (-4ix2 + x3))(4i + x) = 0

Reorder the terms:
(-4ix2 + -4i2x + 16i3 + x3)(4i + x) = 0
(-4ix2 + -4i2x + 16i3 + x3)(4i + x) = 0

Multiply (-4ix2 + -4i2x + 16i3 + x3) * (4i + x)
(-4ix2 * (4i + x) + -4i2x * (4i + x) + 16i3 * (4i + x) + x3(4i + x)) = 0
((4i * -4ix2 + x * -4ix2) + -4i2x * (4i + x) + 16i3 * (4i + x) + x3(4i + x)) = 0

Reorder the terms:
((-4ix3 + -16i2x2) + -4i2x * (4i + x) + 16i3 * (4i + x) + x3(4i + x)) = 0
((-4ix3 + -16i2x2) + -4i2x * (4i + x) + 16i3 * (4i + x) + x3(4i + x)) = 0
(-4ix3 + -16i2x2 + (4i * -4i2x + x * -4i2x) + 16i3 * (4i + x) + x3(4i + x)) = 0

Reorder the terms:
(-4ix3 + -16i2x2 + (-4i2x2 + -16i3x) + 16i3 * (4i + x) + x3(4i + x)) = 0
(-4ix3 + -16i2x2 + (-4i2x2 + -16i3x) + 16i3 * (4i + x) + x3(4i + x)) = 0
(-4ix3 + -16i2x2 + -4i2x2 + -16i3x + (4i * 16i3 + x * 16i3) + x3(4i + x)) = 0

Reorder the terms:
(-4ix3 + -16i2x2 + -4i2x2 + -16i3x + (16i3x + 64i4) + x3(4i + x)) = 0
(-4ix3 + -16i2x2 + -4i2x2 + -16i3x + (16i3x + 64i4) + x3(4i + x)) = 0
(-4ix3 + -16i2x2 + -4i2x2 + -16i3x + 16i3x + 64i4 + (4i * x3 + x * x3)) = 0
(-4ix3 + -16i2x2 + -4i2x2 + -16i3x + 16i3x + 64i4 + (4ix3 + x4)) = 0

Reorder the terms:
(-4ix3 + 4ix3 + -16i2x2 + -4i2x2 + -16i3x + 16i3x + 64i4 + x4) = 0

Combine like terms: -4ix3 + 4ix3 = 0
(0 + -16i2x2 + -4i2x2 + -16i3x + 16i3x + 64i4 + x4) = 0
(-16i2x2 + -4i2x2 + -16i3x + 16i3x + 64i4 + x4) = 0

Combine like terms: -16i2x2 + -4i2x2 = -20i2x2
(-20i2x2 + -16i3x + 16i3x + 64i4 + x4) = 0

Combine like terms: -16i3x + 16i3x = 0
(-20i2x2 + 0 + 64i4 + x4) = 0
(-20i2x2 + 64i4 + x4) = 0

Solving
-20i2x2 + 64i4 + x4 = 0

Solving for variable 'i'.

Factor a trinomial.
(4i2 + -1x2)(16i2 + -1x2) = 0

Factor a difference between two squares.
((2i + x)(2i + -1x))(16i2 + -1x2) = 0

Factor a difference between two squares.
((4i + x)(4i + -1x))(2i + x)(2i + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
2i + -1x = 0

Solving
2i + -1x = 0

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

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

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

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

Simplifying
i = 0.5x

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

Simplifying
4i + x = 0

Solving
4i + x = 0

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

Add '-1x' to each side of the equation.
4i + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
4i + 0 = 0 + -1x
4i = 0 + -1x
Remove the zero:
4i = -1x

Divide each side by '4'.
i = -0.25x

Simplifying
i = -0.25x

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

Simplifying
4i + -1x = 0

Solving
4i + -1x = 0

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

Add 'x' to each side of the equation.
4i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
4i + 0 = 0 + x
4i = 0 + x
Remove the zero:
4i = x

Divide each side by '4'.
i = 0.25x

Simplifying
i = 0.25x
Solution
i = {-0.5x, 0.5x, -0.25x, 0.25x}

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