f(x)=(x+3+2i)(x-3+2i)(x-4)(x-4)

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Solution for f(x)=(x+3+2i)(x-3+2i)(x-4)(x-4) equation: 


Simplifying
f(x) = (x + 3 + 2i)(x + -3 + 2i)(x + -4)(x + -4)

Multiply f * x
fx = (x + 3 + 2i)(x + -3 + 2i)(x + -4)(x + -4)

Reorder the terms:
fx = (3 + 2i + x)(x + -3 + 2i)(x + -4)(x + -4)

Reorder the terms:
fx = (3 + 2i + x)(-3 + 2i + x)(x + -4)(x + -4)

Reorder the terms:
fx = (3 + 2i + x)(-3 + 2i + x)(-4 + x)(x + -4)

Reorder the terms:
fx = (3 + 2i + x)(-3 + 2i + x)(-4 + x)(-4 + x)

Multiply (3 + 2i + x) * (-3 + 2i + x)
fx = (3(-3 + 2i + x) + 2i * (-3 + 2i + x) + x(-3 + 2i + x))(-4 + x)(-4 + x)
fx = ((-3 * 3 + 2i * 3 + x * 3) + 2i * (-3 + 2i + x) + x(-3 + 2i + x))(-4 + x)(-4 + x)
fx = ((-9 + 6i + 3x) + 2i * (-3 + 2i + x) + x(-3 + 2i + x))(-4 + x)(-4 + x)
fx = (-9 + 6i + 3x + (-3 * 2i + 2i * 2i + x * 2i) + x(-3 + 2i + x))(-4 + x)(-4 + x)

Reorder the terms:
fx = (-9 + 6i + 3x + (-6i + 2ix + 4i2) + x(-3 + 2i + x))(-4 + x)(-4 + x)
fx = (-9 + 6i + 3x + (-6i + 2ix + 4i2) + x(-3 + 2i + x))(-4 + x)(-4 + x)
fx = (-9 + 6i + 3x + -6i + 2ix + 4i2 + (-3 * x + 2i * x + x * x))(-4 + x)(-4 + x)

Reorder the terms:
fx = (-9 + 6i + 3x + -6i + 2ix + 4i2 + (2ix + -3x + x2))(-4 + x)(-4 + x)
fx = (-9 + 6i + 3x + -6i + 2ix + 4i2 + (2ix + -3x + x2))(-4 + x)(-4 + x)

Reorder the terms:
fx = (-9 + 6i + -6i + 2ix + 2ix + 4i2 + 3x + -3x + x2)(-4 + x)(-4 + x)

Combine like terms: 6i + -6i = 0
fx = (-9 + 0 + 2ix + 2ix + 4i2 + 3x + -3x + x2)(-4 + x)(-4 + x)
fx = (-9 + 2ix + 2ix + 4i2 + 3x + -3x + x2)(-4 + x)(-4 + x)

Combine like terms: 2ix + 2ix = 4ix
fx = (-9 + 4ix + 4i2 + 3x + -3x + x2)(-4 + x)(-4 + x)

Combine like terms: 3x + -3x = 0
fx = (-9 + 4ix + 4i2 + 0 + x2)(-4 + x)(-4 + x)
fx = (-9 + 4ix + 4i2 + x2)(-4 + x)(-4 + x)

Multiply (-9 + 4ix + 4i2 + x2) * (-4 + x)
fx = (-9(-4 + x) + 4ix * (-4 + x) + 4i2 * (-4 + x) + x2(-4 + x))(-4 + x)
fx = ((-4 * -9 + x * -9) + 4ix * (-4 + x) + 4i2 * (-4 + x) + x2(-4 + x))(-4 + x)
fx = ((36 + -9x) + 4ix * (-4 + x) + 4i2 * (-4 + x) + x2(-4 + x))(-4 + x)
fx = (36 + -9x + (-4 * 4ix + x * 4ix) + 4i2 * (-4 + x) + x2(-4 + x))(-4 + x)
fx = (36 + -9x + (-16ix + 4ix2) + 4i2 * (-4 + x) + x2(-4 + x))(-4 + x)
fx = (36 + -9x + -16ix + 4ix2 + (-4 * 4i2 + x * 4i2) + x2(-4 + x))(-4 + x)
fx = (36 + -9x + -16ix + 4ix2 + (-16i2 + 4i2x) + x2(-4 + x))(-4 + x)
fx = (36 + -9x + -16ix + 4ix2 + -16i2 + 4i2x + (-4 * x2 + x * x2))(-4 + x)
fx = (36 + -9x + -16ix + 4ix2 + -16i2 + 4i2x + (-4x2 + x3))(-4 + x)

Reorder the terms:
fx = (36 + -16ix + 4ix2 + -16i2 + 4i2x + -9x + -4x2 + x3)(-4 + x)
fx = (36 + -16ix + 4ix2 + -16i2 + 4i2x + -9x + -4x2 + x3)(-4 + x)

Multiply (36 + -16ix + 4ix2 + -16i2 + 4i2x + -9x + -4x2 + x3) * (-4 + x)
fx = (36(-4 + x) + -16ix * (-4 + x) + 4ix2 * (-4 + x) + -16i2 * (-4 + x) + 4i2x * (-4 + x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = ((-4 * 36 + x * 36) + -16ix * (-4 + x) + 4ix2 * (-4 + x) + -16i2 * (-4 + x) + 4i2x * (-4 + x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = ((-144 + 36x) + -16ix * (-4 + x) + 4ix2 * (-4 + x) + -16i2 * (-4 + x) + 4i2x * (-4 + x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + (-4 * -16ix + x * -16ix) + 4ix2 * (-4 + x) + -16i2 * (-4 + x) + 4i2x * (-4 + x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + (64ix + -16ix2) + 4ix2 * (-4 + x) + -16i2 * (-4 + x) + 4i2x * (-4 + x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + (-4 * 4ix2 + x * 4ix2) + -16i2 * (-4 + x) + 4i2x * (-4 + x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + (-16ix2 + 4ix3) + -16i2 * (-4 + x) + 4i2x * (-4 + x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + (-4 * -16i2 + x * -16i2) + 4i2x * (-4 + x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + (64i2 + -16i2x) + 4i2x * (-4 + x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + 64i2 + -16i2x + (-4 * 4i2x + x * 4i2x) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + 64i2 + -16i2x + (-16i2x + 4i2x2) + -9x * (-4 + x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + 64i2 + -16i2x + -16i2x + 4i2x2 + (-4 * -9x + x * -9x) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + 64i2 + -16i2x + -16i2x + 4i2x2 + (36x + -9x2) + -4x2 * (-4 + x) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + 64i2 + -16i2x + -16i2x + 4i2x2 + 36x + -9x2 + (-4 * -4x2 + x * -4x2) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + 64i2 + -16i2x + -16i2x + 4i2x2 + 36x + -9x2 + (16x2 + -4x3) + x3(-4 + x))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + 64i2 + -16i2x + -16i2x + 4i2x2 + 36x + -9x2 + 16x2 + -4x3 + (-4 * x3 + x * x3))
fx = (-144 + 36x + 64ix + -16ix2 + -16ix2 + 4ix3 + 64i2 + -16i2x + -16i2x + 4i2x2 + 36x + -9x2 + 16x2 + -4x3 + (-4x3 + x4))

Reorder the terms:
fx = (-144 + 64ix + -16ix2 + -16ix2 + 4ix3 + 64i2 + -16i2x + -16i2x + 4i2x2 + 36x + 36x + -9x2 + 16x2 + -4x3 + -4x3 + x4)

Combine like terms: -16ix2 + -16ix2 = -32ix2
fx = (-144 + 64ix + -32ix2 + 4ix3 + 64i2 + -16i2x + -16i2x + 4i2x2 + 36x + 36x + -9x2 + 16x2 + -4x3 + -4x3 + x4)

Combine like terms: -16i2x + -16i2x = -32i2x
fx = (-144 + 64ix + -32ix2 + 4ix3 + 64i2 + -32i2x + 4i2x2 + 36x + 36x + -9x2 + 16x2 + -4x3 + -4x3 + x4)

Combine like terms: 36x + 36x = 72x
fx = (-144 + 64ix + -32ix2 + 4ix3 + 64i2 + -32i2x + 4i2x2 + 72x + -9x2 + 16x2 + -4x3 + -4x3 + x4)

Combine like terms: -9x2 + 16x2 = 7x2
fx = (-144 + 64ix + -32ix2 + 4ix3 + 64i2 + -32i2x + 4i2x2 + 72x + 7x2 + -4x3 + -4x3 + x4)

Combine like terms: -4x3 + -4x3 = -8x3
fx = (-144 + 64ix + -32ix2 + 4ix3 + 64i2 + -32i2x + 4i2x2 + 72x + 7x2 + -8x3 + x4)

Solving
fx = -144 + 64ix + -32ix2 + 4ix3 + 64i2 + -32i2x + 4i2x2 + 72x + 7x2 + -8x3 + x4

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.
f = -144x-1 + 64i + -32ix + 4ix2 + 64i2x-1 + -32i2 + 4i2x + 72 + 7x + -8x2 + x3

Simplifying
f = -144x-1 + 64i + -32ix + 4ix2 + 64i2x-1 + -32i2 + 4i2x + 72 + 7x + -8x2 + x3

Reorder the terms:
f = 72 + 64i + -32ix + 4ix2 + -32i2 + 64i2x-1 + 4i2x + -144x-1 + 7x + -8x2 + x3

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