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

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


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

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

Remove parenthesis around (4i)
fx = (x + -1 * 4i)(x + -1(4i))(x + -2)

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

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

Remove parenthesis around (4i)
fx = (-4i + x)(x + -1 * 4i)(x + -2)

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

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

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

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

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

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

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

Multiply (-8ix + 16i2 + x2) * (-2 + x)
fx = (-8ix * (-2 + x) + 16i2 * (-2 + x) + x2(-2 + x))
fx = ((-2 * -8ix + x * -8ix) + 16i2 * (-2 + x) + x2(-2 + x))
fx = ((16ix + -8ix2) + 16i2 * (-2 + x) + x2(-2 + x))
fx = (16ix + -8ix2 + (-2 * 16i2 + x * 16i2) + x2(-2 + x))
fx = (16ix + -8ix2 + (-32i2 + 16i2x) + x2(-2 + x))
fx = (16ix + -8ix2 + -32i2 + 16i2x + (-2 * x2 + x * x2))
fx = (16ix + -8ix2 + -32i2 + 16i2x + (-2x2 + x3))
fx = (16ix + -8ix2 + -32i2 + 16i2x + -2x2 + x3)

Solving
fx = 16ix + -8ix2 + -32i2 + 16i2x + -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 = 16i + -8ix + -32i2x-1 + 16i2 + -2x + x2

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

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

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