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

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


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

Reorder the terms:
0 = (2 + x)(x + -1(3 + i))(x + (3 + -1i))
0 = (2 + x)(x + (3 * -1 + i * -1))(x + (3 + -1i))
0 = (2 + x)(x + (-3 + -1i))(x + (3 + -1i))

Reorder the terms:
0 = (2 + x)(-3 + -1i + x)(x + (3 + -1i))

Remove parenthesis around (3 + -1i)
0 = (2 + x)(-3 + -1i + x)(x + 3 + -1i)

Reorder the terms:
0 = (2 + x)(-3 + -1i + x)(3 + -1i + x)

Multiply (2 + x) * (-3 + -1i + x)
0 = (2(-3 + -1i + x) + x(-3 + -1i + x))(3 + -1i + x)
0 = ((-3 * 2 + -1i * 2 + x * 2) + x(-3 + -1i + x))(3 + -1i + x)
0 = ((-6 + -2i + 2x) + x(-3 + -1i + x))(3 + -1i + x)
0 = (-6 + -2i + 2x + (-3 * x + -1i * x + x * x))(3 + -1i + x)

Reorder the terms:
0 = (-6 + -2i + 2x + (-1ix + -3x + x2))(3 + -1i + x)
0 = (-6 + -2i + 2x + (-1ix + -3x + x2))(3 + -1i + x)

Reorder the terms:
0 = (-6 + -2i + -1ix + 2x + -3x + x2)(3 + -1i + x)

Combine like terms: 2x + -3x = -1x
0 = (-6 + -2i + -1ix + -1x + x2)(3 + -1i + x)

Multiply (-6 + -2i + -1ix + -1x + x2) * (3 + -1i + x)
0 = (-6(3 + -1i + x) + -2i * (3 + -1i + x) + -1ix * (3 + -1i + x) + -1x * (3 + -1i + x) + x2(3 + -1i + x))
0 = ((3 * -6 + -1i * -6 + x * -6) + -2i * (3 + -1i + x) + -1ix * (3 + -1i + x) + -1x * (3 + -1i + x) + x2(3 + -1i + x))
0 = ((-18 + 6i + -6x) + -2i * (3 + -1i + x) + -1ix * (3 + -1i + x) + -1x * (3 + -1i + x) + x2(3 + -1i + x))
0 = (-18 + 6i + -6x + (3 * -2i + -1i * -2i + x * -2i) + -1ix * (3 + -1i + x) + -1x * (3 + -1i + x) + x2(3 + -1i + x))

Reorder the terms:
0 = (-18 + 6i + -6x + (-6i + -2ix + 2i2) + -1ix * (3 + -1i + x) + -1x * (3 + -1i + x) + x2(3 + -1i + x))
0 = (-18 + 6i + -6x + (-6i + -2ix + 2i2) + -1ix * (3 + -1i + x) + -1x * (3 + -1i + x) + x2(3 + -1i + x))
0 = (-18 + 6i + -6x + -6i + -2ix + 2i2 + (3 * -1ix + -1i * -1ix + x * -1ix) + -1x * (3 + -1i + x) + x2(3 + -1i + x))

Reorder the terms:
0 = (-18 + 6i + -6x + -6i + -2ix + 2i2 + (-3ix + -1ix2 + 1i2x) + -1x * (3 + -1i + x) + x2(3 + -1i + x))
0 = (-18 + 6i + -6x + -6i + -2ix + 2i2 + (-3ix + -1ix2 + 1i2x) + -1x * (3 + -1i + x) + x2(3 + -1i + x))
0 = (-18 + 6i + -6x + -6i + -2ix + 2i2 + -3ix + -1ix2 + 1i2x + (3 * -1x + -1i * -1x + x * -1x) + x2(3 + -1i + x))

Reorder the terms:
0 = (-18 + 6i + -6x + -6i + -2ix + 2i2 + -3ix + -1ix2 + 1i2x + (1ix + -3x + -1x2) + x2(3 + -1i + x))
0 = (-18 + 6i + -6x + -6i + -2ix + 2i2 + -3ix + -1ix2 + 1i2x + (1ix + -3x + -1x2) + x2(3 + -1i + x))
0 = (-18 + 6i + -6x + -6i + -2ix + 2i2 + -3ix + -1ix2 + 1i2x + 1ix + -3x + -1x2 + (3 * x2 + -1i * x2 + x * x2))

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

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

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

Combine like terms: -2ix + -3ix = -5ix
0 = (-18 + -5ix + 1ix + -1ix2 + -1ix2 + 2i2 + 1i2x + -6x + -3x + -1x2 + 3x2 + x3)

Combine like terms: -5ix + 1ix = -4ix
0 = (-18 + -4ix + -1ix2 + -1ix2 + 2i2 + 1i2x + -6x + -3x + -1x2 + 3x2 + x3)

Combine like terms: -1ix2 + -1ix2 = -2ix2
0 = (-18 + -4ix + -2ix2 + 2i2 + 1i2x + -6x + -3x + -1x2 + 3x2 + x3)

Combine like terms: -6x + -3x = -9x
0 = (-18 + -4ix + -2ix2 + 2i2 + 1i2x + -9x + -1x2 + 3x2 + x3)

Combine like terms: -1x2 + 3x2 = 2x2
0 = (-18 + -4ix + -2ix2 + 2i2 + 1i2x + -9x + 2x2 + x3)

Solving
0 = -18 + -4ix + -2ix2 + 2i2 + 1i2x + -9x + 2x2 + x3

Solving for variable 'i'.

Combine like terms: 0 + 18 = 18
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = -18 + -4ix + -2ix2 + 2i2 + 1i2x + -9x + 2x2 + x3 + 18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3

Reorder the terms:
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = -18 + 18 + -4ix + 4ix + -2ix2 + 2ix2 + 2i2 + -2i2 + 1i2x + -1i2x + -9x + 9x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -18 + 18 = 0
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 0 + -4ix + 4ix + -2ix2 + 2ix2 + 2i2 + -2i2 + 1i2x + -1i2x + -9x + 9x + 2x2 + -2x2 + x3 + -1x3
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = -4ix + 4ix + -2ix2 + 2ix2 + 2i2 + -2i2 + 1i2x + -1i2x + -9x + 9x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -4ix + 4ix = 0
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 0 + -2ix2 + 2ix2 + 2i2 + -2i2 + 1i2x + -1i2x + -9x + 9x + 2x2 + -2x2 + x3 + -1x3
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = -2ix2 + 2ix2 + 2i2 + -2i2 + 1i2x + -1i2x + -9x + 9x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -2ix2 + 2ix2 = 0
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 0 + 2i2 + -2i2 + 1i2x + -1i2x + -9x + 9x + 2x2 + -2x2 + x3 + -1x3
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 2i2 + -2i2 + 1i2x + -1i2x + -9x + 9x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: 2i2 + -2i2 = 0
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 0 + 1i2x + -1i2x + -9x + 9x + 2x2 + -2x2 + x3 + -1x3
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 1i2x + -1i2x + -9x + 9x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: 1i2x + -1i2x = 0
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 0 + -9x + 9x + 2x2 + -2x2 + x3 + -1x3
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = -9x + 9x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -9x + 9x = 0
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 0 + 2x2 + -2x2 + x3 + -1x3
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 2x2 + -2x2 + x3 + -1x3

Combine like terms: 2x2 + -2x2 = 0
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 0 + x3 + -1x3
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
18 + 4ix + 2ix2 + -2i2 + -1i2x + 9x + -2x2 + -1x3 = 0

The solution to this equation could not be determined.

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