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

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Solution for f(x)=(x-(1+i))(x-(1-i))(x-2) equation: 


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

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

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

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

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

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

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

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

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

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

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

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

Multiply (1 + -1i2 + -2x + x2) * (-2 + x)
fx = (1(-2 + x) + -1i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))
fx = ((-2 * 1 + x * 1) + -1i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))
fx = ((-2 + 1x) + -1i2 * (-2 + x) + -2x * (-2 + x) + x2(-2 + x))
fx = (-2 + 1x + (-2 * -1i2 + x * -1i2) + -2x * (-2 + x) + x2(-2 + x))
fx = (-2 + 1x + (2i2 + -1i2x) + -2x * (-2 + x) + x2(-2 + x))
fx = (-2 + 1x + 2i2 + -1i2x + (-2 * -2x + x * -2x) + x2(-2 + x))
fx = (-2 + 1x + 2i2 + -1i2x + (4x + -2x2) + x2(-2 + x))
fx = (-2 + 1x + 2i2 + -1i2x + 4x + -2x2 + (-2 * x2 + x * x2))
fx = (-2 + 1x + 2i2 + -1i2x + 4x + -2x2 + (-2x2 + x3))

Reorder the terms:
fx = (-2 + 2i2 + -1i2x + 1x + 4x + -2x2 + -2x2 + x3)

Combine like terms: 1x + 4x = 5x
fx = (-2 + 2i2 + -1i2x + 5x + -2x2 + -2x2 + x3)

Combine like terms: -2x2 + -2x2 = -4x2
fx = (-2 + 2i2 + -1i2x + 5x + -4x2 + x3)

Solving
fx = -2 + 2i2 + -1i2x + 5x + -4x2 + 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 = -2x-1 + 2i2x-1 + -1i2 + 5 + -4x + x2

Simplifying
f = -2x-1 + 2i2x-1 + -1i2 + 5 + -4x + x2

Reorder the terms:
f = 5 + -1i2 + 2i2x-1 + -2x-1 + -4x + x2

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