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

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

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

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

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

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

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

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

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

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

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