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

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


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

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

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

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

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

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

Reorder the terms:
y = (1 + -2i + -1x + (2i + -2ix + -4i2) + x(-1 + 2i + x))(-1 + x)(2 + x)
y = (1 + -2i + -1x + (2i + -2ix + -4i2) + x(-1 + 2i + x))(-1 + x)(2 + x)
y = (1 + -2i + -1x + 2i + -2ix + -4i2 + (-1 * x + 2i * x + x * x))(-1 + x)(2 + x)

Reorder the terms:
y = (1 + -2i + -1x + 2i + -2ix + -4i2 + (2ix + -1x + x2))(-1 + x)(2 + x)
y = (1 + -2i + -1x + 2i + -2ix + -4i2 + (2ix + -1x + x2))(-1 + x)(2 + x)

Reorder the terms:
y = (1 + -2i + 2i + -2ix + 2ix + -4i2 + -1x + -1x + x2)(-1 + x)(2 + x)

Combine like terms: -2i + 2i = 0
y = (1 + 0 + -2ix + 2ix + -4i2 + -1x + -1x + x2)(-1 + x)(2 + x)
y = (1 + -2ix + 2ix + -4i2 + -1x + -1x + x2)(-1 + x)(2 + x)

Combine like terms: -2ix + 2ix = 0
y = (1 + 0 + -4i2 + -1x + -1x + x2)(-1 + x)(2 + x)
y = (1 + -4i2 + -1x + -1x + x2)(-1 + x)(2 + x)

Combine like terms: -1x + -1x = -2x
y = (1 + -4i2 + -2x + x2)(-1 + x)(2 + x)

Multiply (1 + -4i2 + -2x + x2) * (-1 + x)
y = (1(-1 + x) + -4i2 * (-1 + x) + -2x * (-1 + x) + x2(-1 + x))(2 + x)
y = ((-1 * 1 + x * 1) + -4i2 * (-1 + x) + -2x * (-1 + x) + x2(-1 + x))(2 + x)
y = ((-1 + 1x) + -4i2 * (-1 + x) + -2x * (-1 + x) + x2(-1 + x))(2 + x)
y = (-1 + 1x + (-1 * -4i2 + x * -4i2) + -2x * (-1 + x) + x2(-1 + x))(2 + x)
y = (-1 + 1x + (4i2 + -4i2x) + -2x * (-1 + x) + x2(-1 + x))(2 + x)
y = (-1 + 1x + 4i2 + -4i2x + (-1 * -2x + x * -2x) + x2(-1 + x))(2 + x)
y = (-1 + 1x + 4i2 + -4i2x + (2x + -2x2) + x2(-1 + x))(2 + x)
y = (-1 + 1x + 4i2 + -4i2x + 2x + -2x2 + (-1 * x2 + x * x2))(2 + x)
y = (-1 + 1x + 4i2 + -4i2x + 2x + -2x2 + (-1x2 + x3))(2 + x)

Reorder the terms:
y = (-1 + 4i2 + -4i2x + 1x + 2x + -2x2 + -1x2 + x3)(2 + x)

Combine like terms: 1x + 2x = 3x
y = (-1 + 4i2 + -4i2x + 3x + -2x2 + -1x2 + x3)(2 + x)

Combine like terms: -2x2 + -1x2 = -3x2
y = (-1 + 4i2 + -4i2x + 3x + -3x2 + x3)(2 + x)

Multiply (-1 + 4i2 + -4i2x + 3x + -3x2 + x3) * (2 + x)
y = (-1(2 + x) + 4i2 * (2 + x) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x))
y = ((2 * -1 + x * -1) + 4i2 * (2 + x) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x))
y = ((-2 + -1x) + 4i2 * (2 + x) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x))
y = (-2 + -1x + (2 * 4i2 + x * 4i2) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x))
y = (-2 + -1x + (8i2 + 4i2x) + -4i2x * (2 + x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x))
y = (-2 + -1x + 8i2 + 4i2x + (2 * -4i2x + x * -4i2x) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x))
y = (-2 + -1x + 8i2 + 4i2x + (-8i2x + -4i2x2) + 3x * (2 + x) + -3x2 * (2 + x) + x3(2 + x))
y = (-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + (2 * 3x + x * 3x) + -3x2 * (2 + x) + x3(2 + x))
y = (-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + (6x + 3x2) + -3x2 * (2 + x) + x3(2 + x))
y = (-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + 6x + 3x2 + (2 * -3x2 + x * -3x2) + x3(2 + x))
y = (-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + 6x + 3x2 + (-6x2 + -3x3) + x3(2 + x))
y = (-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + 6x + 3x2 + -6x2 + -3x3 + (2 * x3 + x * x3))
y = (-2 + -1x + 8i2 + 4i2x + -8i2x + -4i2x2 + 6x + 3x2 + -6x2 + -3x3 + (2x3 + x4))

Reorder the terms:
y = (-2 + 8i2 + 4i2x + -8i2x + -4i2x2 + -1x + 6x + 3x2 + -6x2 + -3x3 + 2x3 + x4)

Combine like terms: 4i2x + -8i2x = -4i2x
y = (-2 + 8i2 + -4i2x + -4i2x2 + -1x + 6x + 3x2 + -6x2 + -3x3 + 2x3 + x4)

Combine like terms: -1x + 6x = 5x
y = (-2 + 8i2 + -4i2x + -4i2x2 + 5x + 3x2 + -6x2 + -3x3 + 2x3 + x4)

Combine like terms: 3x2 + -6x2 = -3x2
y = (-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -3x3 + 2x3 + x4)

Combine like terms: -3x3 + 2x3 = -1x3
y = (-2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4)

Solving
y = -2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4

Solving for variable 'y'.

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

Simplifying
y = -2 + 8i2 + -4i2x + -4i2x2 + 5x + -3x2 + -1x3 + x4

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