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

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


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

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

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

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

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

Multiply (2 + x) * (2 + x)
y = (2(2 + x) + x(2 + x))(i + x)(-1i + x)
y = ((2 * 2 + x * 2) + x(2 + x))(i + x)(-1i + x)
y = ((4 + 2x) + x(2 + x))(i + x)(-1i + x)
y = (4 + 2x + (2 * x + x * x))(i + x)(-1i + x)
y = (4 + 2x + (2x + x2))(i + x)(-1i + x)

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

Multiply (4 + 4x + x2) * (i + x)
y = (4(i + x) + 4x * (i + x) + x2(i + x))(-1i + x)
y = ((i * 4 + x * 4) + 4x * (i + x) + x2(i + x))(-1i + x)
y = ((4i + 4x) + 4x * (i + x) + x2(i + x))(-1i + x)
y = (4i + 4x + (i * 4x + x * 4x) + x2(i + x))(-1i + x)
y = (4i + 4x + (4ix + 4x2) + x2(i + x))(-1i + x)
y = (4i + 4x + 4ix + 4x2 + (i * x2 + x * x2))(-1i + x)
y = (4i + 4x + 4ix + 4x2 + (ix2 + x3))(-1i + x)

Reorder the terms:
y = (4i + 4ix + ix2 + 4x + 4x2 + x3)(-1i + x)
y = (4i + 4ix + ix2 + 4x + 4x2 + x3)(-1i + x)

Multiply (4i + 4ix + ix2 + 4x + 4x2 + x3) * (-1i + x)
y = (4i * (-1i + x) + 4ix * (-1i + x) + ix2(-1i + x) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))
y = ((-1i * 4i + x * 4i) + 4ix * (-1i + x) + ix2(-1i + x) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))

Reorder the terms:
y = ((4ix + -4i2) + 4ix * (-1i + x) + ix2(-1i + x) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))
y = ((4ix + -4i2) + 4ix * (-1i + x) + ix2(-1i + x) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))
y = (4ix + -4i2 + (-1i * 4ix + x * 4ix) + ix2(-1i + x) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))

Reorder the terms:
y = (4ix + -4i2 + (4ix2 + -4i2x) + ix2(-1i + x) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))
y = (4ix + -4i2 + (4ix2 + -4i2x) + ix2(-1i + x) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))
y = (4ix + -4i2 + 4ix2 + -4i2x + (-1i * ix2 + x * ix2) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))

Reorder the terms:
y = (4ix + -4i2 + 4ix2 + -4i2x + (ix3 + -1i2x2) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))
y = (4ix + -4i2 + 4ix2 + -4i2x + (ix3 + -1i2x2) + 4x * (-1i + x) + 4x2 * (-1i + x) + x3(-1i + x))
y = (4ix + -4i2 + 4ix2 + -4i2x + ix3 + -1i2x2 + (-1i * 4x + x * 4x) + 4x2 * (-1i + x) + x3(-1i + x))
y = (4ix + -4i2 + 4ix2 + -4i2x + ix3 + -1i2x2 + (-4ix + 4x2) + 4x2 * (-1i + x) + x3(-1i + x))
y = (4ix + -4i2 + 4ix2 + -4i2x + ix3 + -1i2x2 + -4ix + 4x2 + (-1i * 4x2 + x * 4x2) + x3(-1i + x))
y = (4ix + -4i2 + 4ix2 + -4i2x + ix3 + -1i2x2 + -4ix + 4x2 + (-4ix2 + 4x3) + x3(-1i + x))
y = (4ix + -4i2 + 4ix2 + -4i2x + ix3 + -1i2x2 + -4ix + 4x2 + -4ix2 + 4x3 + (-1i * x3 + x * x3))
y = (4ix + -4i2 + 4ix2 + -4i2x + ix3 + -1i2x2 + -4ix + 4x2 + -4ix2 + 4x3 + (-1ix3 + x4))

Reorder the terms:
y = (4ix + -4ix + 4ix2 + -4ix2 + ix3 + -1ix3 + -4i2 + -4i2x + -1i2x2 + 4x2 + 4x3 + x4)

Combine like terms: 4ix + -4ix = 0
y = (0 + 4ix2 + -4ix2 + ix3 + -1ix3 + -4i2 + -4i2x + -1i2x2 + 4x2 + 4x3 + x4)
y = (4ix2 + -4ix2 + ix3 + -1ix3 + -4i2 + -4i2x + -1i2x2 + 4x2 + 4x3 + x4)

Combine like terms: 4ix2 + -4ix2 = 0
y = (0 + ix3 + -1ix3 + -4i2 + -4i2x + -1i2x2 + 4x2 + 4x3 + x4)
y = (ix3 + -1ix3 + -4i2 + -4i2x + -1i2x2 + 4x2 + 4x3 + x4)

Combine like terms: ix3 + -1ix3 = 0
y = (0 + -4i2 + -4i2x + -1i2x2 + 4x2 + 4x3 + x4)
y = (-4i2 + -4i2x + -1i2x2 + 4x2 + 4x3 + x4)

Solving
y = -4i2 + -4i2x + -1i2x2 + 4x2 + 4x3 + x4

Solving for variable 'y'.

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

Simplifying
y = -4i2 + -4i2x + -1i2x2 + 4x2 + 4x3 + x4

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