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

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


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

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

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

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

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

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

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

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

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

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

Solving
y = 1 + -4i2 + -2x + x2

Solving for variable 'y'.

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

Simplifying
y = 1 + -4i2 + -2x + x2

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