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 = 0
y = (-4 + 0 + x2)(i + x)(-1i + x)
y = (-4 + x2)(i + x)(-1i + x)

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

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

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

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

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

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

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

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

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

Solving for variable 'y'.

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

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

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