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

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Solution for (x-2)(x-(2-3i))(x+(2+3i))=0 equation: 


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

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

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

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

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

Multiply (-2 + x) * (-2 + 3i + x)
(-2(-2 + 3i + x) + x(-2 + 3i + x))(2 + 3i + x) = 0
((-2 * -2 + 3i * -2 + x * -2) + x(-2 + 3i + x))(2 + 3i + x) = 0
((4 + -6i + -2x) + x(-2 + 3i + x))(2 + 3i + x) = 0
(4 + -6i + -2x + (-2 * x + 3i * x + x * x))(2 + 3i + x) = 0

Reorder the terms:
(4 + -6i + -2x + (3ix + -2x + x2))(2 + 3i + x) = 0
(4 + -6i + -2x + (3ix + -2x + x2))(2 + 3i + x) = 0

Reorder the terms:
(4 + -6i + 3ix + -2x + -2x + x2)(2 + 3i + x) = 0

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

Multiply (4 + -6i + 3ix + -4x + x2) * (2 + 3i + x)
(4(2 + 3i + x) + -6i * (2 + 3i + x) + 3ix * (2 + 3i + x) + -4x * (2 + 3i + x) + x2(2 + 3i + x)) = 0
((2 * 4 + 3i * 4 + x * 4) + -6i * (2 + 3i + x) + 3ix * (2 + 3i + x) + -4x * (2 + 3i + x) + x2(2 + 3i + x)) = 0
((8 + 12i + 4x) + -6i * (2 + 3i + x) + 3ix * (2 + 3i + x) + -4x * (2 + 3i + x) + x2(2 + 3i + x)) = 0
(8 + 12i + 4x + (2 * -6i + 3i * -6i + x * -6i) + 3ix * (2 + 3i + x) + -4x * (2 + 3i + x) + x2(2 + 3i + x)) = 0

Reorder the terms:
(8 + 12i + 4x + (-12i + -6ix + -18i2) + 3ix * (2 + 3i + x) + -4x * (2 + 3i + x) + x2(2 + 3i + x)) = 0
(8 + 12i + 4x + (-12i + -6ix + -18i2) + 3ix * (2 + 3i + x) + -4x * (2 + 3i + x) + x2(2 + 3i + x)) = 0
(8 + 12i + 4x + -12i + -6ix + -18i2 + (2 * 3ix + 3i * 3ix + x * 3ix) + -4x * (2 + 3i + x) + x2(2 + 3i + x)) = 0

Reorder the terms:
(8 + 12i + 4x + -12i + -6ix + -18i2 + (6ix + 3ix2 + 9i2x) + -4x * (2 + 3i + x) + x2(2 + 3i + x)) = 0
(8 + 12i + 4x + -12i + -6ix + -18i2 + (6ix + 3ix2 + 9i2x) + -4x * (2 + 3i + x) + x2(2 + 3i + x)) = 0
(8 + 12i + 4x + -12i + -6ix + -18i2 + 6ix + 3ix2 + 9i2x + (2 * -4x + 3i * -4x + x * -4x) + x2(2 + 3i + x)) = 0

Reorder the terms:
(8 + 12i + 4x + -12i + -6ix + -18i2 + 6ix + 3ix2 + 9i2x + (-12ix + -8x + -4x2) + x2(2 + 3i + x)) = 0
(8 + 12i + 4x + -12i + -6ix + -18i2 + 6ix + 3ix2 + 9i2x + (-12ix + -8x + -4x2) + x2(2 + 3i + x)) = 0
(8 + 12i + 4x + -12i + -6ix + -18i2 + 6ix + 3ix2 + 9i2x + -12ix + -8x + -4x2 + (2 * x2 + 3i * x2 + x * x2)) = 0

Reorder the terms:
(8 + 12i + 4x + -12i + -6ix + -18i2 + 6ix + 3ix2 + 9i2x + -12ix + -8x + -4x2 + (3ix2 + 2x2 + x3)) = 0
(8 + 12i + 4x + -12i + -6ix + -18i2 + 6ix + 3ix2 + 9i2x + -12ix + -8x + -4x2 + (3ix2 + 2x2 + x3)) = 0

Reorder the terms:
(8 + 12i + -12i + -6ix + 6ix + -12ix + 3ix2 + 3ix2 + -18i2 + 9i2x + 4x + -8x + -4x2 + 2x2 + x3) = 0

Combine like terms: 12i + -12i = 0
(8 + 0 + -6ix + 6ix + -12ix + 3ix2 + 3ix2 + -18i2 + 9i2x + 4x + -8x + -4x2 + 2x2 + x3) = 0
(8 + -6ix + 6ix + -12ix + 3ix2 + 3ix2 + -18i2 + 9i2x + 4x + -8x + -4x2 + 2x2 + x3) = 0

Combine like terms: -6ix + 6ix = 0
(8 + 0 + -12ix + 3ix2 + 3ix2 + -18i2 + 9i2x + 4x + -8x + -4x2 + 2x2 + x3) = 0
(8 + -12ix + 3ix2 + 3ix2 + -18i2 + 9i2x + 4x + -8x + -4x2 + 2x2 + x3) = 0

Combine like terms: 3ix2 + 3ix2 = 6ix2
(8 + -12ix + 6ix2 + -18i2 + 9i2x + 4x + -8x + -4x2 + 2x2 + x3) = 0

Combine like terms: 4x + -8x = -4x
(8 + -12ix + 6ix2 + -18i2 + 9i2x + -4x + -4x2 + 2x2 + x3) = 0

Combine like terms: -4x2 + 2x2 = -2x2
(8 + -12ix + 6ix2 + -18i2 + 9i2x + -4x + -2x2 + x3) = 0

Solving
8 + -12ix + 6ix2 + -18i2 + 9i2x + -4x + -2x2 + x3 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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