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

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


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

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

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

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

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

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

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

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

Combine like terms: 1x + -3x = -2x
fx = (-3 + -1i + -1ix + -2x + x2)(-3 + i + x)

Multiply (-3 + -1i + -1ix + -2x + x2) * (-3 + i + x)
fx = (-3(-3 + i + x) + -1i * (-3 + i + x) + -1ix * (-3 + i + x) + -2x * (-3 + i + x) + x2(-3 + i + x))
fx = ((-3 * -3 + i * -3 + x * -3) + -1i * (-3 + i + x) + -1ix * (-3 + i + x) + -2x * (-3 + i + x) + x2(-3 + i + x))
fx = ((9 + -3i + -3x) + -1i * (-3 + i + x) + -1ix * (-3 + i + x) + -2x * (-3 + i + x) + x2(-3 + i + x))
fx = (9 + -3i + -3x + (-3 * -1i + i * -1i + x * -1i) + -1ix * (-3 + i + x) + -2x * (-3 + i + x) + x2(-3 + i + x))

Reorder the terms:
fx = (9 + -3i + -3x + (3i + -1ix + -1i2) + -1ix * (-3 + i + x) + -2x * (-3 + i + x) + x2(-3 + i + x))
fx = (9 + -3i + -3x + (3i + -1ix + -1i2) + -1ix * (-3 + i + x) + -2x * (-3 + i + x) + x2(-3 + i + x))
fx = (9 + -3i + -3x + 3i + -1ix + -1i2 + (-3 * -1ix + i * -1ix + x * -1ix) + -2x * (-3 + i + x) + x2(-3 + i + x))

Reorder the terms:
fx = (9 + -3i + -3x + 3i + -1ix + -1i2 + (3ix + -1ix2 + -1i2x) + -2x * (-3 + i + x) + x2(-3 + i + x))
fx = (9 + -3i + -3x + 3i + -1ix + -1i2 + (3ix + -1ix2 + -1i2x) + -2x * (-3 + i + x) + x2(-3 + i + x))
fx = (9 + -3i + -3x + 3i + -1ix + -1i2 + 3ix + -1ix2 + -1i2x + (-3 * -2x + i * -2x + x * -2x) + x2(-3 + i + x))

Reorder the terms:
fx = (9 + -3i + -3x + 3i + -1ix + -1i2 + 3ix + -1ix2 + -1i2x + (-2ix + 6x + -2x2) + x2(-3 + i + x))
fx = (9 + -3i + -3x + 3i + -1ix + -1i2 + 3ix + -1ix2 + -1i2x + (-2ix + 6x + -2x2) + x2(-3 + i + x))
fx = (9 + -3i + -3x + 3i + -1ix + -1i2 + 3ix + -1ix2 + -1i2x + -2ix + 6x + -2x2 + (-3 * x2 + i * x2 + x * x2))

Reorder the terms:
fx = (9 + -3i + -3x + 3i + -1ix + -1i2 + 3ix + -1ix2 + -1i2x + -2ix + 6x + -2x2 + (ix2 + -3x2 + x3))
fx = (9 + -3i + -3x + 3i + -1ix + -1i2 + 3ix + -1ix2 + -1i2x + -2ix + 6x + -2x2 + (ix2 + -3x2 + x3))

Reorder the terms:
fx = (9 + -3i + 3i + -1ix + 3ix + -2ix + -1ix2 + ix2 + -1i2 + -1i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: -3i + 3i = 0
fx = (9 + 0 + -1ix + 3ix + -2ix + -1ix2 + ix2 + -1i2 + -1i2x + -3x + 6x + -2x2 + -3x2 + x3)
fx = (9 + -1ix + 3ix + -2ix + -1ix2 + ix2 + -1i2 + -1i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: -1ix + 3ix = 2ix
fx = (9 + 2ix + -2ix + -1ix2 + ix2 + -1i2 + -1i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: 2ix + -2ix = 0
fx = (9 + 0 + -1ix2 + ix2 + -1i2 + -1i2x + -3x + 6x + -2x2 + -3x2 + x3)
fx = (9 + -1ix2 + ix2 + -1i2 + -1i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: -1ix2 + ix2 = 0
fx = (9 + 0 + -1i2 + -1i2x + -3x + 6x + -2x2 + -3x2 + x3)
fx = (9 + -1i2 + -1i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: -3x + 6x = 3x
fx = (9 + -1i2 + -1i2x + 3x + -2x2 + -3x2 + x3)

Combine like terms: -2x2 + -3x2 = -5x2
fx = (9 + -1i2 + -1i2x + 3x + -5x2 + x3)

Solving
fx = 9 + -1i2 + -1i2x + 3x + -5x2 + 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 + -1i2x-1 + -1i2 + 3 + -5x + x2

Simplifying
f = 9x-1 + -1i2x-1 + -1i2 + 3 + -5x + x2

Reorder the terms:
f = 3 + -1i2 + -1i2x-1 + 9x-1 + -5x + x2

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