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

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


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

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

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

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

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

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

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

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

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

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

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

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

Multiply (4 + -1i2 + -4x + x2) * (-4 + x)
fx = (4(-4 + x) + -1i2 * (-4 + x) + -4x * (-4 + x) + x2(-4 + x))
fx = ((-4 * 4 + x * 4) + -1i2 * (-4 + x) + -4x * (-4 + x) + x2(-4 + x))
fx = ((-16 + 4x) + -1i2 * (-4 + x) + -4x * (-4 + x) + x2(-4 + x))
fx = (-16 + 4x + (-4 * -1i2 + x * -1i2) + -4x * (-4 + x) + x2(-4 + x))
fx = (-16 + 4x + (4i2 + -1i2x) + -4x * (-4 + x) + x2(-4 + x))
fx = (-16 + 4x + 4i2 + -1i2x + (-4 * -4x + x * -4x) + x2(-4 + x))
fx = (-16 + 4x + 4i2 + -1i2x + (16x + -4x2) + x2(-4 + x))
fx = (-16 + 4x + 4i2 + -1i2x + 16x + -4x2 + (-4 * x2 + x * x2))
fx = (-16 + 4x + 4i2 + -1i2x + 16x + -4x2 + (-4x2 + x3))

Reorder the terms:
fx = (-16 + 4i2 + -1i2x + 4x + 16x + -4x2 + -4x2 + x3)

Combine like terms: 4x + 16x = 20x
fx = (-16 + 4i2 + -1i2x + 20x + -4x2 + -4x2 + x3)

Combine like terms: -4x2 + -4x2 = -8x2
fx = (-16 + 4i2 + -1i2x + 20x + -8x2 + x3)

Solving
fx = -16 + 4i2 + -1i2x + 20x + -8x2 + 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 = -16x-1 + 4i2x-1 + -1i2 + 20 + -8x + x2

Simplifying
f = -16x-1 + 4i2x-1 + -1i2 + 20 + -8x + x2

Reorder the terms:
f = 20 + -1i2 + 4i2x-1 + -16x-1 + -8x + x2

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