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

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Solution for (x-1)(x+2)(x+2i)(x-2i)= equation: 


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

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

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

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

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

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

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

Multiply (-2 + 1x + x2) * (2i + x)
(-2(2i + x) + 1x * (2i + x) + x2(2i + x))(-2i + x) = 0
((2i * -2 + x * -2) + 1x * (2i + x) + x2(2i + x))(-2i + x) = 0
((-4i + -2x) + 1x * (2i + x) + x2(2i + x))(-2i + x) = 0
(-4i + -2x + (2i * 1x + x * 1x) + x2(2i + x))(-2i + x) = 0
(-4i + -2x + (2ix + 1x2) + x2(2i + x))(-2i + x) = 0
(-4i + -2x + 2ix + 1x2 + (2i * x2 + x * x2))(-2i + x) = 0
(-4i + -2x + 2ix + 1x2 + (2ix2 + x3))(-2i + x) = 0

Reorder the terms:
(-4i + 2ix + 2ix2 + -2x + 1x2 + x3)(-2i + x) = 0
(-4i + 2ix + 2ix2 + -2x + 1x2 + x3)(-2i + x) = 0

Multiply (-4i + 2ix + 2ix2 + -2x + 1x2 + x3) * (-2i + x)
(-4i * (-2i + x) + 2ix * (-2i + x) + 2ix2 * (-2i + x) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0
((-2i * -4i + x * -4i) + 2ix * (-2i + x) + 2ix2 * (-2i + x) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0

Reorder the terms:
((-4ix + 8i2) + 2ix * (-2i + x) + 2ix2 * (-2i + x) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0
((-4ix + 8i2) + 2ix * (-2i + x) + 2ix2 * (-2i + x) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0
(-4ix + 8i2 + (-2i * 2ix + x * 2ix) + 2ix2 * (-2i + x) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0

Reorder the terms:
(-4ix + 8i2 + (2ix2 + -4i2x) + 2ix2 * (-2i + x) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0
(-4ix + 8i2 + (2ix2 + -4i2x) + 2ix2 * (-2i + x) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0
(-4ix + 8i2 + 2ix2 + -4i2x + (-2i * 2ix2 + x * 2ix2) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0

Reorder the terms:
(-4ix + 8i2 + 2ix2 + -4i2x + (2ix3 + -4i2x2) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0
(-4ix + 8i2 + 2ix2 + -4i2x + (2ix3 + -4i2x2) + -2x * (-2i + x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0
(-4ix + 8i2 + 2ix2 + -4i2x + 2ix3 + -4i2x2 + (-2i * -2x + x * -2x) + 1x2 * (-2i + x) + x3(-2i + x)) = 0
(-4ix + 8i2 + 2ix2 + -4i2x + 2ix3 + -4i2x2 + (4ix + -2x2) + 1x2 * (-2i + x) + x3(-2i + x)) = 0
(-4ix + 8i2 + 2ix2 + -4i2x + 2ix3 + -4i2x2 + 4ix + -2x2 + (-2i * 1x2 + x * 1x2) + x3(-2i + x)) = 0
(-4ix + 8i2 + 2ix2 + -4i2x + 2ix3 + -4i2x2 + 4ix + -2x2 + (-2ix2 + 1x3) + x3(-2i + x)) = 0
(-4ix + 8i2 + 2ix2 + -4i2x + 2ix3 + -4i2x2 + 4ix + -2x2 + -2ix2 + 1x3 + (-2i * x3 + x * x3)) = 0
(-4ix + 8i2 + 2ix2 + -4i2x + 2ix3 + -4i2x2 + 4ix + -2x2 + -2ix2 + 1x3 + (-2ix3 + x4)) = 0

Reorder the terms:
(-4ix + 4ix + 2ix2 + -2ix2 + 2ix3 + -2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4) = 0

Combine like terms: -4ix + 4ix = 0
(0 + 2ix2 + -2ix2 + 2ix3 + -2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4) = 0
(2ix2 + -2ix2 + 2ix3 + -2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4) = 0

Combine like terms: 2ix2 + -2ix2 = 0
(0 + 2ix3 + -2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4) = 0
(2ix3 + -2ix3 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4) = 0

Combine like terms: 2ix3 + -2ix3 = 0
(0 + 8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4) = 0
(8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4) = 0

Solving
8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + x4 = 0

Solving for variable 'i'.

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

Add '2x2' to each side of the equation.
8i2 + -4i2x + -4i2x2 + -2x2 + 1x3 + 2x2 + x4 = 0 + 2x2

Reorder the terms:
8i2 + -4i2x + -4i2x2 + -2x2 + 2x2 + 1x3 + x4 = 0 + 2x2

Combine like terms: -2x2 + 2x2 = 0
8i2 + -4i2x + -4i2x2 + 0 + 1x3 + x4 = 0 + 2x2
8i2 + -4i2x + -4i2x2 + 1x3 + x4 = 0 + 2x2
Remove the zero:
8i2 + -4i2x + -4i2x2 + 1x3 + x4 = 2x2

Add '-1x3' to each side of the equation.
8i2 + -4i2x + -4i2x2 + 1x3 + -1x3 + x4 = 2x2 + -1x3

Combine like terms: 1x3 + -1x3 = 0
8i2 + -4i2x + -4i2x2 + 0 + x4 = 2x2 + -1x3
8i2 + -4i2x + -4i2x2 + x4 = 2x2 + -1x3

Add '-1x4' to each side of the equation.
8i2 + -4i2x + -4i2x2 + x4 + -1x4 = 2x2 + -1x3 + -1x4

Combine like terms: x4 + -1x4 = 0
8i2 + -4i2x + -4i2x2 + 0 = 2x2 + -1x3 + -1x4
8i2 + -4i2x + -4i2x2 = 2x2 + -1x3 + -1x4

Reorder the terms:
8i2 + -4i2x + -4i2x2 + -2x2 + x3 + x4 = 2x2 + -2x2 + -1x3 + x3 + -1x4 + x4

Combine like terms: 2x2 + -2x2 = 0
8i2 + -4i2x + -4i2x2 + -2x2 + x3 + x4 = 0 + -1x3 + x3 + -1x4 + x4
8i2 + -4i2x + -4i2x2 + -2x2 + x3 + x4 = -1x3 + x3 + -1x4 + x4

Combine like terms: -1x3 + x3 = 0
8i2 + -4i2x + -4i2x2 + -2x2 + x3 + x4 = 0 + -1x4 + x4
8i2 + -4i2x + -4i2x2 + -2x2 + x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
8i2 + -4i2x + -4i2x2 + -2x2 + x3 + x4 = 0

The solution to this equation could not be determined.

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