f(x)=1(x+-3+2i)(x+-3+2i)(x+1)(x+-2)

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Solution for f(x)=1(x+-3+2i)(x+-3+2i)(x+1)(x+-2) equation: 


Simplifying
f(x) = 1(x + -3 + 2i)(x + -3 + 2i)(x + 1)(x + -2)

Multiply f * x
fx = 1(x + -3 + 2i)(x + -3 + 2i)(x + 1)(x + -2)

Reorder the terms:
fx = 1(-3 + 2i + x)(x + -3 + 2i)(x + 1)(x + -2)

Reorder the terms:
fx = 1(-3 + 2i + x)(-3 + 2i + x)(x + 1)(x + -2)

Reorder the terms:
fx = 1(-3 + 2i + x)(-3 + 2i + x)(1 + x)(x + -2)

Reorder the terms:
fx = 1(-3 + 2i + x)(-3 + 2i + x)(1 + x)(-2 + x)

Multiply (-3 + 2i + x) * (-3 + 2i + x)
fx = 1(-3(-3 + 2i + x) + 2i * (-3 + 2i + x) + x(-3 + 2i + x))(1 + x)(-2 + x)
fx = 1((-3 * -3 + 2i * -3 + x * -3) + 2i * (-3 + 2i + x) + x(-3 + 2i + x))(1 + x)(-2 + x)
fx = 1((9 + -6i + -3x) + 2i * (-3 + 2i + x) + x(-3 + 2i + x))(1 + x)(-2 + x)
fx = 1(9 + -6i + -3x + (-3 * 2i + 2i * 2i + x * 2i) + x(-3 + 2i + x))(1 + x)(-2 + x)

Reorder the terms:
fx = 1(9 + -6i + -3x + (-6i + 2ix + 4i2) + x(-3 + 2i + x))(1 + x)(-2 + x)
fx = 1(9 + -6i + -3x + (-6i + 2ix + 4i2) + x(-3 + 2i + x))(1 + x)(-2 + x)
fx = 1(9 + -6i + -3x + -6i + 2ix + 4i2 + (-3 * x + 2i * x + x * x))(1 + x)(-2 + x)

Reorder the terms:
fx = 1(9 + -6i + -3x + -6i + 2ix + 4i2 + (2ix + -3x + x2))(1 + x)(-2 + x)
fx = 1(9 + -6i + -3x + -6i + 2ix + 4i2 + (2ix + -3x + x2))(1 + x)(-2 + x)

Reorder the terms:
fx = 1(9 + -6i + -6i + 2ix + 2ix + 4i2 + -3x + -3x + x2)(1 + x)(-2 + x)

Combine like terms: -6i + -6i = -12i
fx = 1(9 + -12i + 2ix + 2ix + 4i2 + -3x + -3x + x2)(1 + x)(-2 + x)

Combine like terms: 2ix + 2ix = 4ix
fx = 1(9 + -12i + 4ix + 4i2 + -3x + -3x + x2)(1 + x)(-2 + x)

Combine like terms: -3x + -3x = -6x
fx = 1(9 + -12i + 4ix + 4i2 + -6x + x2)(1 + x)(-2 + x)

Multiply (9 + -12i + 4ix + 4i2 + -6x + x2) * (1 + x)
fx = 1(9(1 + x) + -12i * (1 + x) + 4ix * (1 + x) + 4i2 * (1 + x) + -6x * (1 + x) + x2(1 + x))(-2 + x)
fx = 1((1 * 9 + x * 9) + -12i * (1 + x) + 4ix * (1 + x) + 4i2 * (1 + x) + -6x * (1 + x) + x2(1 + x))(-2 + x)
fx = 1((9 + 9x) + -12i * (1 + x) + 4ix * (1 + x) + 4i2 * (1 + x) + -6x * (1 + x) + x2(1 + x))(-2 + x)
fx = 1(9 + 9x + (1 * -12i + x * -12i) + 4ix * (1 + x) + 4i2 * (1 + x) + -6x * (1 + x) + x2(1 + x))(-2 + x)
fx = 1(9 + 9x + (-12i + -12ix) + 4ix * (1 + x) + 4i2 * (1 + x) + -6x * (1 + x) + x2(1 + x))(-2 + x)
fx = 1(9 + 9x + -12i + -12ix + (1 * 4ix + x * 4ix) + 4i2 * (1 + x) + -6x * (1 + x) + x2(1 + x))(-2 + x)
fx = 1(9 + 9x + -12i + -12ix + (4ix + 4ix2) + 4i2 * (1 + x) + -6x * (1 + x) + x2(1 + x))(-2 + x)
fx = 1(9 + 9x + -12i + -12ix + 4ix + 4ix2 + (1 * 4i2 + x * 4i2) + -6x * (1 + x) + x2(1 + x))(-2 + x)
fx = 1(9 + 9x + -12i + -12ix + 4ix + 4ix2 + (4i2 + 4i2x) + -6x * (1 + x) + x2(1 + x))(-2 + x)
fx = 1(9 + 9x + -12i + -12ix + 4ix + 4ix2 + 4i2 + 4i2x + (1 * -6x + x * -6x) + x2(1 + x))(-2 + x)
fx = 1(9 + 9x + -12i + -12ix + 4ix + 4ix2 + 4i2 + 4i2x + (-6x + -6x2) + x2(1 + x))(-2 + x)
fx = 1(9 + 9x + -12i + -12ix + 4ix + 4ix2 + 4i2 + 4i2x + -6x + -6x2 + (1 * x2 + x * x2))(-2 + x)
fx = 1(9 + 9x + -12i + -12ix + 4ix + 4ix2 + 4i2 + 4i2x + -6x + -6x2 + (1x2 + x3))(-2 + x)

Reorder the terms:
fx = 1(9 + -12i + -12ix + 4ix + 4ix2 + 4i2 + 4i2x + 9x + -6x + -6x2 + 1x2 + x3)(-2 + x)

Combine like terms: -12ix + 4ix = -8ix
fx = 1(9 + -12i + -8ix + 4ix2 + 4i2 + 4i2x + 9x + -6x + -6x2 + 1x2 + x3)(-2 + x)

Combine like terms: 9x + -6x = 3x
fx = 1(9 + -12i + -8ix + 4ix2 + 4i2 + 4i2x + 3x + -6x2 + 1x2 + x3)(-2 + x)

Combine like terms: -6x2 + 1x2 = -5x2
fx = 1(9 + -12i + -8ix + 4ix2 + 4i2 + 4i2x + 3x + -5x2 + x3)(-2 + x)

Multiply (9 + -12i + -8ix + 4ix2 + 4i2 + 4i2x + 3x + -5x2 + x3) * (-2 + x)
fx = 1(9(-2 + x) + -12i * (-2 + x) + -8ix * (-2 + x) + 4ix2 * (-2 + x) + 4i2 * (-2 + x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1((-2 * 9 + x * 9) + -12i * (-2 + x) + -8ix * (-2 + x) + 4ix2 * (-2 + x) + 4i2 * (-2 + x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1((-18 + 9x) + -12i * (-2 + x) + -8ix * (-2 + x) + 4ix2 * (-2 + x) + 4i2 * (-2 + x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + (-2 * -12i + x * -12i) + -8ix * (-2 + x) + 4ix2 * (-2 + x) + 4i2 * (-2 + x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + (24i + -12ix) + -8ix * (-2 + x) + 4ix2 * (-2 + x) + 4i2 * (-2 + x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + (-2 * -8ix + x * -8ix) + 4ix2 * (-2 + x) + 4i2 * (-2 + x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + (16ix + -8ix2) + 4ix2 * (-2 + x) + 4i2 * (-2 + x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + (-2 * 4ix2 + x * 4ix2) + 4i2 * (-2 + x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + (-8ix2 + 4ix3) + 4i2 * (-2 + x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + (-2 * 4i2 + x * 4i2) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + (-8i2 + 4i2x) + 4i2x * (-2 + x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + (-2 * 4i2x + x * 4i2x) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + (-8i2x + 4i2x2) + 3x * (-2 + x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + -8i2x + 4i2x2 + (-2 * 3x + x * 3x) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + -8i2x + 4i2x2 + (-6x + 3x2) + -5x2 * (-2 + x) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + -8i2x + 4i2x2 + -6x + 3x2 + (-2 * -5x2 + x * -5x2) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + -8i2x + 4i2x2 + -6x + 3x2 + (10x2 + -5x3) + x3(-2 + x))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + -8i2x + 4i2x2 + -6x + 3x2 + 10x2 + -5x3 + (-2 * x3 + x * x3))
fx = 1(-18 + 9x + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + -8i2x + 4i2x2 + -6x + 3x2 + 10x2 + -5x3 + (-2x3 + x4))

Reorder the terms:
fx = 1(-18 + 24i + -12ix + 16ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + -8i2x + 4i2x2 + 9x + -6x + 3x2 + 10x2 + -5x3 + -2x3 + x4)

Combine like terms: -12ix + 16ix = 4ix
fx = 1(-18 + 24i + 4ix + -8ix2 + -8ix2 + 4ix3 + -8i2 + 4i2x + -8i2x + 4i2x2 + 9x + -6x + 3x2 + 10x2 + -5x3 + -2x3 + x4)

Combine like terms: -8ix2 + -8ix2 = -16ix2
fx = 1(-18 + 24i + 4ix + -16ix2 + 4ix3 + -8i2 + 4i2x + -8i2x + 4i2x2 + 9x + -6x + 3x2 + 10x2 + -5x3 + -2x3 + x4)

Combine like terms: 4i2x + -8i2x = -4i2x
fx = 1(-18 + 24i + 4ix + -16ix2 + 4ix3 + -8i2 + -4i2x + 4i2x2 + 9x + -6x + 3x2 + 10x2 + -5x3 + -2x3 + x4)

Combine like terms: 9x + -6x = 3x
fx = 1(-18 + 24i + 4ix + -16ix2 + 4ix3 + -8i2 + -4i2x + 4i2x2 + 3x + 3x2 + 10x2 + -5x3 + -2x3 + x4)

Combine like terms: 3x2 + 10x2 = 13x2
fx = 1(-18 + 24i + 4ix + -16ix2 + 4ix3 + -8i2 + -4i2x + 4i2x2 + 3x + 13x2 + -5x3 + -2x3 + x4)

Combine like terms: -5x3 + -2x3 = -7x3
fx = 1(-18 + 24i + 4ix + -16ix2 + 4ix3 + -8i2 + -4i2x + 4i2x2 + 3x + 13x2 + -7x3 + x4)
fx = (-18 * 1 + 24i * 1 + 4ix * 1 + -16ix2 * 1 + 4ix3 * 1 + -8i2 * 1 + -4i2x * 1 + 4i2x2 * 1 + 3x * 1 + 13x2 * 1 + -7x3 * 1 + x4 * 1)
fx = (-18 + 24i + 4ix + -16ix2 + 4ix3 + -8i2 + -4i2x + 4i2x2 + 3x + 13x2 + -7x3 + 1x4)

Solving
fx = -18 + 24i + 4ix + -16ix2 + 4ix3 + -8i2 + -4i2x + 4i2x2 + 3x + 13x2 + -7x3 + 1x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -18x-1 + 24ix-1 + 4i + -16ix + 4ix2 + -8i2x-1 + -4i2 + 4i2x + 3 + 13x + -7x2 + x3

Simplifying
f = -18x-1 + 24ix-1 + 4i + -16ix + 4ix2 + -8i2x-1 + -4i2 + 4i2x + 3 + 13x + -7x2 + x3

Reorder the terms:
f = 3 + 4i + 24ix-1 + -16ix + 4ix2 + -4i2 + -8i2x-1 + 4i2x + -18x-1 + 13x + -7x2 + x3

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