f(x)=(x+3)(x-6-2i)(x-6+2i)

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Solution for f(x)=(x+3)(x-6-2i)(x-6+2i) equation: 


Simplifying
f(x) = (x + 3)(x + -6 + -2i)(x + -6 + 2i)

Multiply f * x
fx = (x + 3)(x + -6 + -2i)(x + -6 + 2i)

Reorder the terms:
fx = (3 + x)(x + -6 + -2i)(x + -6 + 2i)

Reorder the terms:
fx = (3 + x)(-6 + -2i + x)(x + -6 + 2i)

Reorder the terms:
fx = (3 + x)(-6 + -2i + x)(-6 + 2i + x)

Multiply (3 + x) * (-6 + -2i + x)
fx = (3(-6 + -2i + x) + x(-6 + -2i + x))(-6 + 2i + x)
fx = ((-6 * 3 + -2i * 3 + x * 3) + x(-6 + -2i + x))(-6 + 2i + x)
fx = ((-18 + -6i + 3x) + x(-6 + -2i + x))(-6 + 2i + x)
fx = (-18 + -6i + 3x + (-6 * x + -2i * x + x * x))(-6 + 2i + x)

Reorder the terms:
fx = (-18 + -6i + 3x + (-2ix + -6x + x2))(-6 + 2i + x)
fx = (-18 + -6i + 3x + (-2ix + -6x + x2))(-6 + 2i + x)

Reorder the terms:
fx = (-18 + -6i + -2ix + 3x + -6x + x2)(-6 + 2i + x)

Combine like terms: 3x + -6x = -3x
fx = (-18 + -6i + -2ix + -3x + x2)(-6 + 2i + x)

Multiply (-18 + -6i + -2ix + -3x + x2) * (-6 + 2i + x)
fx = (-18(-6 + 2i + x) + -6i * (-6 + 2i + x) + -2ix * (-6 + 2i + x) + -3x * (-6 + 2i + x) + x2(-6 + 2i + x))
fx = ((-6 * -18 + 2i * -18 + x * -18) + -6i * (-6 + 2i + x) + -2ix * (-6 + 2i + x) + -3x * (-6 + 2i + x) + x2(-6 + 2i + x))
fx = ((108 + -36i + -18x) + -6i * (-6 + 2i + x) + -2ix * (-6 + 2i + x) + -3x * (-6 + 2i + x) + x2(-6 + 2i + x))
fx = (108 + -36i + -18x + (-6 * -6i + 2i * -6i + x * -6i) + -2ix * (-6 + 2i + x) + -3x * (-6 + 2i + x) + x2(-6 + 2i + x))

Reorder the terms:
fx = (108 + -36i + -18x + (36i + -6ix + -12i2) + -2ix * (-6 + 2i + x) + -3x * (-6 + 2i + x) + x2(-6 + 2i + x))
fx = (108 + -36i + -18x + (36i + -6ix + -12i2) + -2ix * (-6 + 2i + x) + -3x * (-6 + 2i + x) + x2(-6 + 2i + x))
fx = (108 + -36i + -18x + 36i + -6ix + -12i2 + (-6 * -2ix + 2i * -2ix + x * -2ix) + -3x * (-6 + 2i + x) + x2(-6 + 2i + x))

Reorder the terms:
fx = (108 + -36i + -18x + 36i + -6ix + -12i2 + (12ix + -2ix2 + -4i2x) + -3x * (-6 + 2i + x) + x2(-6 + 2i + x))
fx = (108 + -36i + -18x + 36i + -6ix + -12i2 + (12ix + -2ix2 + -4i2x) + -3x * (-6 + 2i + x) + x2(-6 + 2i + x))
fx = (108 + -36i + -18x + 36i + -6ix + -12i2 + 12ix + -2ix2 + -4i2x + (-6 * -3x + 2i * -3x + x * -3x) + x2(-6 + 2i + x))

Reorder the terms:
fx = (108 + -36i + -18x + 36i + -6ix + -12i2 + 12ix + -2ix2 + -4i2x + (-6ix + 18x + -3x2) + x2(-6 + 2i + x))
fx = (108 + -36i + -18x + 36i + -6ix + -12i2 + 12ix + -2ix2 + -4i2x + (-6ix + 18x + -3x2) + x2(-6 + 2i + x))
fx = (108 + -36i + -18x + 36i + -6ix + -12i2 + 12ix + -2ix2 + -4i2x + -6ix + 18x + -3x2 + (-6 * x2 + 2i * x2 + x * x2))

Reorder the terms:
fx = (108 + -36i + -18x + 36i + -6ix + -12i2 + 12ix + -2ix2 + -4i2x + -6ix + 18x + -3x2 + (2ix2 + -6x2 + x3))
fx = (108 + -36i + -18x + 36i + -6ix + -12i2 + 12ix + -2ix2 + -4i2x + -6ix + 18x + -3x2 + (2ix2 + -6x2 + x3))

Reorder the terms:
fx = (108 + -36i + 36i + -6ix + 12ix + -6ix + -2ix2 + 2ix2 + -12i2 + -4i2x + -18x + 18x + -3x2 + -6x2 + x3)

Combine like terms: -36i + 36i = 0
fx = (108 + 0 + -6ix + 12ix + -6ix + -2ix2 + 2ix2 + -12i2 + -4i2x + -18x + 18x + -3x2 + -6x2 + x3)
fx = (108 + -6ix + 12ix + -6ix + -2ix2 + 2ix2 + -12i2 + -4i2x + -18x + 18x + -3x2 + -6x2 + x3)

Combine like terms: -6ix + 12ix = 6ix
fx = (108 + 6ix + -6ix + -2ix2 + 2ix2 + -12i2 + -4i2x + -18x + 18x + -3x2 + -6x2 + x3)

Combine like terms: 6ix + -6ix = 0
fx = (108 + 0 + -2ix2 + 2ix2 + -12i2 + -4i2x + -18x + 18x + -3x2 + -6x2 + x3)
fx = (108 + -2ix2 + 2ix2 + -12i2 + -4i2x + -18x + 18x + -3x2 + -6x2 + x3)

Combine like terms: -2ix2 + 2ix2 = 0
fx = (108 + 0 + -12i2 + -4i2x + -18x + 18x + -3x2 + -6x2 + x3)
fx = (108 + -12i2 + -4i2x + -18x + 18x + -3x2 + -6x2 + x3)

Combine like terms: -18x + 18x = 0
fx = (108 + -12i2 + -4i2x + 0 + -3x2 + -6x2 + x3)
fx = (108 + -12i2 + -4i2x + -3x2 + -6x2 + x3)

Combine like terms: -3x2 + -6x2 = -9x2
fx = (108 + -12i2 + -4i2x + -9x2 + x3)

Solving
fx = 108 + -12i2 + -4i2x + -9x2 + 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 = 108x-1 + -12i2x-1 + -4i2 + -9x + x2

Simplifying
f = 108x-1 + -12i2x-1 + -4i2 + -9x + x2

Reorder the terms:
f = -4i2 + -12i2x-1 + 108x-1 + -9x + x2

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