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

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


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

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

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

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

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

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

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

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

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

Multiply (-6 + 2i + 1ix + -1x + x2) * (-3 + -1i + x)
fx = (-6(-3 + -1i + x) + 2i * (-3 + -1i + x) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x))
fx = ((-3 * -6 + -1i * -6 + x * -6) + 2i * (-3 + -1i + x) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x))
fx = ((18 + 6i + -6x) + 2i * (-3 + -1i + x) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x))
fx = (18 + 6i + -6x + (-3 * 2i + -1i * 2i + x * 2i) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x))

Reorder the terms:
fx = (18 + 6i + -6x + (-6i + 2ix + -2i2) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x))
fx = (18 + 6i + -6x + (-6i + 2ix + -2i2) + 1ix * (-3 + -1i + x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x))
fx = (18 + 6i + -6x + -6i + 2ix + -2i2 + (-3 * 1ix + -1i * 1ix + x * 1ix) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x))

Reorder the terms:
fx = (18 + 6i + -6x + -6i + 2ix + -2i2 + (-3ix + 1ix2 + -1i2x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x))
fx = (18 + 6i + -6x + -6i + 2ix + -2i2 + (-3ix + 1ix2 + -1i2x) + -1x * (-3 + -1i + x) + x2(-3 + -1i + x))
fx = (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + (-3 * -1x + -1i * -1x + x * -1x) + x2(-3 + -1i + x))

Reorder the terms:
fx = (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + (1ix + 3x + -1x2) + x2(-3 + -1i + x))
fx = (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + (1ix + 3x + -1x2) + x2(-3 + -1i + x))
fx = (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + 1ix + 3x + -1x2 + (-3 * x2 + -1i * x2 + x * x2))

Reorder the terms:
fx = (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + 1ix + 3x + -1x2 + (-1ix2 + -3x2 + x3))
fx = (18 + 6i + -6x + -6i + 2ix + -2i2 + -3ix + 1ix2 + -1i2x + 1ix + 3x + -1x2 + (-1ix2 + -3x2 + x3))

Reorder the terms:
fx = (18 + 6i + -6i + 2ix + -3ix + 1ix + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3)

Combine like terms: 6i + -6i = 0
fx = (18 + 0 + 2ix + -3ix + 1ix + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3)
fx = (18 + 2ix + -3ix + 1ix + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3)

Combine like terms: 2ix + -3ix = -1ix
fx = (18 + -1ix + 1ix + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3)

Combine like terms: -1ix + 1ix = 0
fx = (18 + 0 + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3)
fx = (18 + 1ix2 + -1ix2 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3)

Combine like terms: 1ix2 + -1ix2 = 0
fx = (18 + 0 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3)
fx = (18 + -2i2 + -1i2x + -6x + 3x + -1x2 + -3x2 + x3)

Combine like terms: -6x + 3x = -3x
fx = (18 + -2i2 + -1i2x + -3x + -1x2 + -3x2 + x3)

Combine like terms: -1x2 + -3x2 = -4x2
fx = (18 + -2i2 + -1i2x + -3x + -4x2 + x3)

Solving
fx = 18 + -2i2 + -1i2x + -3x + -4x2 + 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 = 18x-1 + -2i2x-1 + -1i2 + -3 + -4x + x2

Simplifying
f = 18x-1 + -2i2x-1 + -1i2 + -3 + -4x + x2

Reorder the terms:
f = -3 + -1i2 + -2i2x-1 + 18x-1 + -4x + x2

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