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

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


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

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

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

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

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

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

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

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

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

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

Reorder the terms:
y = (1 + -1i + 1x + 1i + 1ix + -1i2 + (1ix + ix2 + -1i2x) + 2x * (1 + -1i + x) + x2(1 + -1i + x))
y = (1 + -1i + 1x + 1i + 1ix + -1i2 + (1ix + ix2 + -1i2x) + 2x * (1 + -1i + x) + x2(1 + -1i + x))
y = (1 + -1i + 1x + 1i + 1ix + -1i2 + 1ix + ix2 + -1i2x + (1 * 2x + -1i * 2x + x * 2x) + x2(1 + -1i + x))

Reorder the terms:
y = (1 + -1i + 1x + 1i + 1ix + -1i2 + 1ix + ix2 + -1i2x + (-2ix + 2x + 2x2) + x2(1 + -1i + x))
y = (1 + -1i + 1x + 1i + 1ix + -1i2 + 1ix + ix2 + -1i2x + (-2ix + 2x + 2x2) + x2(1 + -1i + x))
y = (1 + -1i + 1x + 1i + 1ix + -1i2 + 1ix + ix2 + -1i2x + -2ix + 2x + 2x2 + (1 * x2 + -1i * x2 + x * x2))

Reorder the terms:
y = (1 + -1i + 1x + 1i + 1ix + -1i2 + 1ix + ix2 + -1i2x + -2ix + 2x + 2x2 + (-1ix2 + 1x2 + x3))
y = (1 + -1i + 1x + 1i + 1ix + -1i2 + 1ix + ix2 + -1i2x + -2ix + 2x + 2x2 + (-1ix2 + 1x2 + x3))

Reorder the terms:
y = (1 + -1i + 1i + 1ix + 1ix + -2ix + ix2 + -1ix2 + -1i2 + -1i2x + 1x + 2x + 2x2 + 1x2 + x3)

Combine like terms: -1i + 1i = 0
y = (1 + 0 + 1ix + 1ix + -2ix + ix2 + -1ix2 + -1i2 + -1i2x + 1x + 2x + 2x2 + 1x2 + x3)
y = (1 + 1ix + 1ix + -2ix + ix2 + -1ix2 + -1i2 + -1i2x + 1x + 2x + 2x2 + 1x2 + x3)

Combine like terms: 1ix + 1ix = 2ix
y = (1 + 2ix + -2ix + ix2 + -1ix2 + -1i2 + -1i2x + 1x + 2x + 2x2 + 1x2 + x3)

Combine like terms: 2ix + -2ix = 0
y = (1 + 0 + ix2 + -1ix2 + -1i2 + -1i2x + 1x + 2x + 2x2 + 1x2 + x3)
y = (1 + ix2 + -1ix2 + -1i2 + -1i2x + 1x + 2x + 2x2 + 1x2 + x3)

Combine like terms: ix2 + -1ix2 = 0
y = (1 + 0 + -1i2 + -1i2x + 1x + 2x + 2x2 + 1x2 + x3)
y = (1 + -1i2 + -1i2x + 1x + 2x + 2x2 + 1x2 + x3)

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

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

Solving
y = 1 + -1i2 + -1i2x + 3x + 3x2 + x3

Solving for variable 'y'.

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

Simplifying
y = 1 + -1i2 + -1i2x + 3x + 3x2 + x3

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