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

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