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

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


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

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

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

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

Multiply (-2 + -4i + x) * (-2 + 4i + x)
fx = (-2(-2 + 4i + x) + -4i * (-2 + 4i + x) + x(-2 + 4i + x))
fx = ((-2 * -2 + 4i * -2 + x * -2) + -4i * (-2 + 4i + x) + x(-2 + 4i + x))
fx = ((4 + -8i + -2x) + -4i * (-2 + 4i + x) + x(-2 + 4i + x))
fx = (4 + -8i + -2x + (-2 * -4i + 4i * -4i + x * -4i) + x(-2 + 4i + x))

Reorder the terms:
fx = (4 + -8i + -2x + (8i + -4ix + -16i2) + x(-2 + 4i + x))
fx = (4 + -8i + -2x + (8i + -4ix + -16i2) + x(-2 + 4i + x))
fx = (4 + -8i + -2x + 8i + -4ix + -16i2 + (-2 * x + 4i * x + x * x))

Reorder the terms:
fx = (4 + -8i + -2x + 8i + -4ix + -16i2 + (4ix + -2x + x2))
fx = (4 + -8i + -2x + 8i + -4ix + -16i2 + (4ix + -2x + x2))

Reorder the terms:
fx = (4 + -8i + 8i + -4ix + 4ix + -16i2 + -2x + -2x + x2)

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

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

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

Solving
fx = 4 + -16i2 + -4x + x2

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 4x-1 + -16i2x-1 + -4 + x

Simplifying
f = 4x-1 + -16i2x-1 + -4 + x

Reorder the terms:
f = -4 + -16i2x-1 + 4x-1 + x

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