f(x)=(x+(3+i))(x-(3+i))(x-1)

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Solution for f(x)=(x+(3+i))(x-(3+i))(x-1) equation: 


Simplifying
f(x) = (x + (3 + i))(x + -1(3 + i))(x + -1)

Multiply f * x
fx = (x + (3 + i))(x + -1(3 + i))(x + -1)

Remove parenthesis around (3 + i)
fx = (x + 3 + i)(x + -1(3 + i))(x + -1)

Reorder the terms:
fx = (3 + i + x)(x + -1(3 + i))(x + -1)
fx = (3 + i + x)(x + (3 * -1 + i * -1))(x + -1)
fx = (3 + i + x)(x + (-3 + -1i))(x + -1)

Reorder the terms:
fx = (3 + i + x)(-3 + -1i + x)(x + -1)

Reorder the terms:
fx = (3 + i + x)(-3 + -1i + x)(-1 + x)

Multiply (3 + i + x) * (-3 + -1i + x)
fx = (3(-3 + -1i + x) + i(-3 + -1i + x) + x(-3 + -1i + x))(-1 + x)
fx = ((-3 * 3 + -1i * 3 + x * 3) + i(-3 + -1i + x) + x(-3 + -1i + x))(-1 + x)
fx = ((-9 + -3i + 3x) + i(-3 + -1i + x) + x(-3 + -1i + x))(-1 + x)
fx = (-9 + -3i + 3x + (-3 * i + -1i * i + x * i) + x(-3 + -1i + x))(-1 + x)

Reorder the terms:
fx = (-9 + -3i + 3x + (-3i + ix + -1i2) + x(-3 + -1i + x))(-1 + x)
fx = (-9 + -3i + 3x + (-3i + ix + -1i2) + x(-3 + -1i + x))(-1 + x)
fx = (-9 + -3i + 3x + -3i + ix + -1i2 + (-3 * x + -1i * x + x * x))(-1 + x)

Reorder the terms:
fx = (-9 + -3i + 3x + -3i + ix + -1i2 + (-1ix + -3x + x2))(-1 + x)
fx = (-9 + -3i + 3x + -3i + ix + -1i2 + (-1ix + -3x + x2))(-1 + x)

Reorder the terms:
fx = (-9 + -3i + -3i + ix + -1ix + -1i2 + 3x + -3x + x2)(-1 + x)

Combine like terms: -3i + -3i = -6i
fx = (-9 + -6i + ix + -1ix + -1i2 + 3x + -3x + x2)(-1 + x)

Combine like terms: ix + -1ix = 0
fx = (-9 + -6i + 0 + -1i2 + 3x + -3x + x2)(-1 + x)
fx = (-9 + -6i + -1i2 + 3x + -3x + x2)(-1 + x)

Combine like terms: 3x + -3x = 0
fx = (-9 + -6i + -1i2 + 0 + x2)(-1 + x)
fx = (-9 + -6i + -1i2 + x2)(-1 + x)

Multiply (-9 + -6i + -1i2 + x2) * (-1 + x)
fx = (-9(-1 + x) + -6i * (-1 + x) + -1i2 * (-1 + x) + x2(-1 + x))
fx = ((-1 * -9 + x * -9) + -6i * (-1 + x) + -1i2 * (-1 + x) + x2(-1 + x))
fx = ((9 + -9x) + -6i * (-1 + x) + -1i2 * (-1 + x) + x2(-1 + x))
fx = (9 + -9x + (-1 * -6i + x * -6i) + -1i2 * (-1 + x) + x2(-1 + x))
fx = (9 + -9x + (6i + -6ix) + -1i2 * (-1 + x) + x2(-1 + x))
fx = (9 + -9x + 6i + -6ix + (-1 * -1i2 + x * -1i2) + x2(-1 + x))
fx = (9 + -9x + 6i + -6ix + (1i2 + -1i2x) + x2(-1 + x))
fx = (9 + -9x + 6i + -6ix + 1i2 + -1i2x + (-1 * x2 + x * x2))
fx = (9 + -9x + 6i + -6ix + 1i2 + -1i2x + (-1x2 + x3))

Reorder the terms:
fx = (9 + 6i + -6ix + 1i2 + -1i2x + -9x + -1x2 + x3)
fx = (9 + 6i + -6ix + 1i2 + -1i2x + -9x + -1x2 + x3)

Solving
fx = 9 + 6i + -6ix + 1i2 + -1i2x + -9x + -1x2 + 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 = 9x-1 + 6ix-1 + -6i + i2x-1 + -1i2 + -9 + -1x + x2

Simplifying
f = 9x-1 + 6ix-1 + -6i + i2x-1 + -1i2 + -9 + -1x + x2

Reorder the terms:
f = -9 + -6i + 6ix-1 + -1i2 + i2x-1 + 9x-1 + -1x + x2

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