0=(x+2)(x+(9+2i))(x-(9+2i))

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Solution for 0=(x+2)(x+(9+2i))(x-(9+2i)) equation: 


Simplifying
0 = (x + 2)(x + (9 + 2i))(x + -1(9 + 2i))

Reorder the terms:
0 = (2 + x)(x + (9 + 2i))(x + -1(9 + 2i))

Remove parenthesis around (9 + 2i)
0 = (2 + x)(x + 9 + 2i)(x + -1(9 + 2i))

Reorder the terms:
0 = (2 + x)(9 + 2i + x)(x + -1(9 + 2i))
0 = (2 + x)(9 + 2i + x)(x + (9 * -1 + 2i * -1))
0 = (2 + x)(9 + 2i + x)(x + (-9 + -2i))

Reorder the terms:
0 = (2 + x)(9 + 2i + x)(-9 + -2i + x)

Multiply (2 + x) * (9 + 2i + x)
0 = (2(9 + 2i + x) + x(9 + 2i + x))(-9 + -2i + x)
0 = ((9 * 2 + 2i * 2 + x * 2) + x(9 + 2i + x))(-9 + -2i + x)
0 = ((18 + 4i + 2x) + x(9 + 2i + x))(-9 + -2i + x)
0 = (18 + 4i + 2x + (9 * x + 2i * x + x * x))(-9 + -2i + x)

Reorder the terms:
0 = (18 + 4i + 2x + (2ix + 9x + x2))(-9 + -2i + x)
0 = (18 + 4i + 2x + (2ix + 9x + x2))(-9 + -2i + x)

Reorder the terms:
0 = (18 + 4i + 2ix + 2x + 9x + x2)(-9 + -2i + x)

Combine like terms: 2x + 9x = 11x
0 = (18 + 4i + 2ix + 11x + x2)(-9 + -2i + x)

Multiply (18 + 4i + 2ix + 11x + x2) * (-9 + -2i + x)
0 = (18(-9 + -2i + x) + 4i * (-9 + -2i + x) + 2ix * (-9 + -2i + x) + 11x * (-9 + -2i + x) + x2(-9 + -2i + x))
0 = ((-9 * 18 + -2i * 18 + x * 18) + 4i * (-9 + -2i + x) + 2ix * (-9 + -2i + x) + 11x * (-9 + -2i + x) + x2(-9 + -2i + x))
0 = ((-162 + -36i + 18x) + 4i * (-9 + -2i + x) + 2ix * (-9 + -2i + x) + 11x * (-9 + -2i + x) + x2(-9 + -2i + x))
0 = (-162 + -36i + 18x + (-9 * 4i + -2i * 4i + x * 4i) + 2ix * (-9 + -2i + x) + 11x * (-9 + -2i + x) + x2(-9 + -2i + x))

Reorder the terms:
0 = (-162 + -36i + 18x + (-36i + 4ix + -8i2) + 2ix * (-9 + -2i + x) + 11x * (-9 + -2i + x) + x2(-9 + -2i + x))
0 = (-162 + -36i + 18x + (-36i + 4ix + -8i2) + 2ix * (-9 + -2i + x) + 11x * (-9 + -2i + x) + x2(-9 + -2i + x))
0 = (-162 + -36i + 18x + -36i + 4ix + -8i2 + (-9 * 2ix + -2i * 2ix + x * 2ix) + 11x * (-9 + -2i + x) + x2(-9 + -2i + x))

Reorder the terms:
0 = (-162 + -36i + 18x + -36i + 4ix + -8i2 + (-18ix + 2ix2 + -4i2x) + 11x * (-9 + -2i + x) + x2(-9 + -2i + x))
0 = (-162 + -36i + 18x + -36i + 4ix + -8i2 + (-18ix + 2ix2 + -4i2x) + 11x * (-9 + -2i + x) + x2(-9 + -2i + x))
0 = (-162 + -36i + 18x + -36i + 4ix + -8i2 + -18ix + 2ix2 + -4i2x + (-9 * 11x + -2i * 11x + x * 11x) + x2(-9 + -2i + x))

Reorder the terms:
0 = (-162 + -36i + 18x + -36i + 4ix + -8i2 + -18ix + 2ix2 + -4i2x + (-22ix + -99x + 11x2) + x2(-9 + -2i + x))
0 = (-162 + -36i + 18x + -36i + 4ix + -8i2 + -18ix + 2ix2 + -4i2x + (-22ix + -99x + 11x2) + x2(-9 + -2i + x))
0 = (-162 + -36i + 18x + -36i + 4ix + -8i2 + -18ix + 2ix2 + -4i2x + -22ix + -99x + 11x2 + (-9 * x2 + -2i * x2 + x * x2))

Reorder the terms:
0 = (-162 + -36i + 18x + -36i + 4ix + -8i2 + -18ix + 2ix2 + -4i2x + -22ix + -99x + 11x2 + (-2ix2 + -9x2 + x3))
0 = (-162 + -36i + 18x + -36i + 4ix + -8i2 + -18ix + 2ix2 + -4i2x + -22ix + -99x + 11x2 + (-2ix2 + -9x2 + x3))

Reorder the terms:
0 = (-162 + -36i + -36i + 4ix + -18ix + -22ix + 2ix2 + -2ix2 + -8i2 + -4i2x + 18x + -99x + 11x2 + -9x2 + x3)

Combine like terms: -36i + -36i = -72i
0 = (-162 + -72i + 4ix + -18ix + -22ix + 2ix2 + -2ix2 + -8i2 + -4i2x + 18x + -99x + 11x2 + -9x2 + x3)

Combine like terms: 4ix + -18ix = -14ix
0 = (-162 + -72i + -14ix + -22ix + 2ix2 + -2ix2 + -8i2 + -4i2x + 18x + -99x + 11x2 + -9x2 + x3)

Combine like terms: -14ix + -22ix = -36ix
0 = (-162 + -72i + -36ix + 2ix2 + -2ix2 + -8i2 + -4i2x + 18x + -99x + 11x2 + -9x2 + x3)

Combine like terms: 2ix2 + -2ix2 = 0
0 = (-162 + -72i + -36ix + 0 + -8i2 + -4i2x + 18x + -99x + 11x2 + -9x2 + x3)
0 = (-162 + -72i + -36ix + -8i2 + -4i2x + 18x + -99x + 11x2 + -9x2 + x3)

Combine like terms: 18x + -99x = -81x
0 = (-162 + -72i + -36ix + -8i2 + -4i2x + -81x + 11x2 + -9x2 + x3)

Combine like terms: 11x2 + -9x2 = 2x2
0 = (-162 + -72i + -36ix + -8i2 + -4i2x + -81x + 2x2 + x3)

Solving
0 = -162 + -72i + -36ix + -8i2 + -4i2x + -81x + 2x2 + x3

Solving for variable 'i'.

Combine like terms: 0 + 162 = 162
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = -162 + -72i + -36ix + -8i2 + -4i2x + -81x + 2x2 + x3 + 162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3

Reorder the terms:
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = -162 + 162 + -72i + 72i + -36ix + 36ix + -8i2 + 8i2 + -4i2x + 4i2x + -81x + 81x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -162 + 162 = 0
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = 0 + -72i + 72i + -36ix + 36ix + -8i2 + 8i2 + -4i2x + 4i2x + -81x + 81x + 2x2 + -2x2 + x3 + -1x3
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = -72i + 72i + -36ix + 36ix + -8i2 + 8i2 + -4i2x + 4i2x + -81x + 81x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -72i + 72i = 0
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = 0 + -36ix + 36ix + -8i2 + 8i2 + -4i2x + 4i2x + -81x + 81x + 2x2 + -2x2 + x3 + -1x3
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = -36ix + 36ix + -8i2 + 8i2 + -4i2x + 4i2x + -81x + 81x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -36ix + 36ix = 0
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = 0 + -8i2 + 8i2 + -4i2x + 4i2x + -81x + 81x + 2x2 + -2x2 + x3 + -1x3
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = -8i2 + 8i2 + -4i2x + 4i2x + -81x + 81x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -8i2 + 8i2 = 0
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = 0 + -4i2x + 4i2x + -81x + 81x + 2x2 + -2x2 + x3 + -1x3
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = -4i2x + 4i2x + -81x + 81x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -4i2x + 4i2x = 0
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = 0 + -81x + 81x + 2x2 + -2x2 + x3 + -1x3
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = -81x + 81x + 2x2 + -2x2 + x3 + -1x3

Combine like terms: -81x + 81x = 0
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = 0 + 2x2 + -2x2 + x3 + -1x3
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = 2x2 + -2x2 + x3 + -1x3

Combine like terms: 2x2 + -2x2 = 0
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = 0 + x3 + -1x3
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
162 + 72i + 36ix + 8i2 + 4i2x + 81x + -2x2 + -1x3 = 0

The solution to this equation could not be determined.

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