f(x)=(x+4+i)(x-4-i)(x-2)

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Solution for f(x)=(x+4+i)(x-4-i)(x-2) equation: 


Simplifying
f(x) = (x + 4 + i)(x + -4 + -1i)(x + -2)

Multiply f * x
fx = (x + 4 + i)(x + -4 + -1i)(x + -2)

Reorder the terms:
fx = (4 + i + x)(x + -4 + -1i)(x + -2)

Reorder the terms:
fx = (4 + i + x)(-4 + -1i + x)(x + -2)

Reorder the terms:
fx = (4 + i + x)(-4 + -1i + x)(-2 + x)

Multiply (4 + i + x) * (-4 + -1i + x)
fx = (4(-4 + -1i + x) + i(-4 + -1i + x) + x(-4 + -1i + x))(-2 + x)
fx = ((-4 * 4 + -1i * 4 + x * 4) + i(-4 + -1i + x) + x(-4 + -1i + x))(-2 + x)
fx = ((-16 + -4i + 4x) + i(-4 + -1i + x) + x(-4 + -1i + x))(-2 + x)
fx = (-16 + -4i + 4x + (-4 * i + -1i * i + x * i) + x(-4 + -1i + x))(-2 + x)

Reorder the terms:
fx = (-16 + -4i + 4x + (-4i + ix + -1i2) + x(-4 + -1i + x))(-2 + x)
fx = (-16 + -4i + 4x + (-4i + ix + -1i2) + x(-4 + -1i + x))(-2 + x)
fx = (-16 + -4i + 4x + -4i + ix + -1i2 + (-4 * x + -1i * x + x * x))(-2 + x)

Reorder the terms:
fx = (-16 + -4i + 4x + -4i + ix + -1i2 + (-1ix + -4x + x2))(-2 + x)
fx = (-16 + -4i + 4x + -4i + ix + -1i2 + (-1ix + -4x + x2))(-2 + x)

Reorder the terms:
fx = (-16 + -4i + -4i + ix + -1ix + -1i2 + 4x + -4x + x2)(-2 + x)

Combine like terms: -4i + -4i = -8i
fx = (-16 + -8i + ix + -1ix + -1i2 + 4x + -4x + x2)(-2 + x)

Combine like terms: ix + -1ix = 0
fx = (-16 + -8i + 0 + -1i2 + 4x + -4x + x2)(-2 + x)
fx = (-16 + -8i + -1i2 + 4x + -4x + x2)(-2 + x)

Combine like terms: 4x + -4x = 0
fx = (-16 + -8i + -1i2 + 0 + x2)(-2 + x)
fx = (-16 + -8i + -1i2 + x2)(-2 + x)

Multiply (-16 + -8i + -1i2 + x2) * (-2 + x)
fx = (-16(-2 + x) + -8i * (-2 + x) + -1i2 * (-2 + x) + x2(-2 + x))
fx = ((-2 * -16 + x * -16) + -8i * (-2 + x) + -1i2 * (-2 + x) + x2(-2 + x))
fx = ((32 + -16x) + -8i * (-2 + x) + -1i2 * (-2 + x) + x2(-2 + x))
fx = (32 + -16x + (-2 * -8i + x * -8i) + -1i2 * (-2 + x) + x2(-2 + x))
fx = (32 + -16x + (16i + -8ix) + -1i2 * (-2 + x) + x2(-2 + x))
fx = (32 + -16x + 16i + -8ix + (-2 * -1i2 + x * -1i2) + x2(-2 + x))
fx = (32 + -16x + 16i + -8ix + (2i2 + -1i2x) + x2(-2 + x))
fx = (32 + -16x + 16i + -8ix + 2i2 + -1i2x + (-2 * x2 + x * x2))
fx = (32 + -16x + 16i + -8ix + 2i2 + -1i2x + (-2x2 + x3))

Reorder the terms:
fx = (32 + 16i + -8ix + 2i2 + -1i2x + -16x + -2x2 + x3)
fx = (32 + 16i + -8ix + 2i2 + -1i2x + -16x + -2x2 + x3)

Solving
fx = 32 + 16i + -8ix + 2i2 + -1i2x + -16x + -2x2 + x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 32x-1 + 16ix-1 + -8i + 2i2x-1 + -1i2 + -16 + -2x + x2

Simplifying
f = 32x-1 + 16ix-1 + -8i + 2i2x-1 + -1i2 + -16 + -2x + x2

Reorder the terms:
f = -16 + -8i + 16ix-1 + -1i2 + 2i2x-1 + 32x-1 + -2x + x2

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