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

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


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

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

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

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

Multiply (3 + x) * (-3 + -1i + x)
(3(-3 + -1i + x) + x(-3 + -1i + x))(-3 + 1i + x) = 0
((-3 * 3 + -1i * 3 + x * 3) + x(-3 + -1i + x))(-3 + 1i + x) = 0
((-9 + -3i + 3x) + x(-3 + -1i + x))(-3 + 1i + x) = 0
(-9 + -3i + 3x + (-3 * x + -1i * x + x * x))(-3 + 1i + x) = 0

Reorder the terms:
(-9 + -3i + 3x + (-1ix + -3x + x2))(-3 + 1i + x) = 0
(-9 + -3i + 3x + (-1ix + -3x + x2))(-3 + 1i + x) = 0

Reorder the terms:
(-9 + -3i + -1ix + 3x + -3x + x2)(-3 + 1i + x) = 0

Combine like terms: 3x + -3x = 0
(-9 + -3i + -1ix + 0 + x2)(-3 + 1i + x) = 0
(-9 + -3i + -1ix + x2)(-3 + 1i + x) = 0

Multiply (-9 + -3i + -1ix + x2) * (-3 + 1i + x)
(-9(-3 + 1i + x) + -3i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + x2(-3 + 1i + x)) = 0
((-3 * -9 + 1i * -9 + x * -9) + -3i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + x2(-3 + 1i + x)) = 0
((27 + -9i + -9x) + -3i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + x2(-3 + 1i + x)) = 0
(27 + -9i + -9x + (-3 * -3i + 1i * -3i + x * -3i) + -1ix * (-3 + 1i + x) + x2(-3 + 1i + x)) = 0

Reorder the terms:
(27 + -9i + -9x + (9i + -3ix + -3i2) + -1ix * (-3 + 1i + x) + x2(-3 + 1i + x)) = 0
(27 + -9i + -9x + (9i + -3ix + -3i2) + -1ix * (-3 + 1i + x) + x2(-3 + 1i + x)) = 0
(27 + -9i + -9x + 9i + -3ix + -3i2 + (-3 * -1ix + 1i * -1ix + x * -1ix) + x2(-3 + 1i + x)) = 0

Reorder the terms:
(27 + -9i + -9x + 9i + -3ix + -3i2 + (3ix + -1ix2 + -1i2x) + x2(-3 + 1i + x)) = 0
(27 + -9i + -9x + 9i + -3ix + -3i2 + (3ix + -1ix2 + -1i2x) + x2(-3 + 1i + x)) = 0
(27 + -9i + -9x + 9i + -3ix + -3i2 + 3ix + -1ix2 + -1i2x + (-3 * x2 + 1i * x2 + x * x2)) = 0

Reorder the terms:
(27 + -9i + -9x + 9i + -3ix + -3i2 + 3ix + -1ix2 + -1i2x + (1ix2 + -3x2 + x3)) = 0
(27 + -9i + -9x + 9i + -3ix + -3i2 + 3ix + -1ix2 + -1i2x + (1ix2 + -3x2 + x3)) = 0

Reorder the terms:
(27 + -9i + 9i + -3ix + 3ix + -1ix2 + 1ix2 + -3i2 + -1i2x + -9x + -3x2 + x3) = 0

Combine like terms: -9i + 9i = 0
(27 + 0 + -3ix + 3ix + -1ix2 + 1ix2 + -3i2 + -1i2x + -9x + -3x2 + x3) = 0
(27 + -3ix + 3ix + -1ix2 + 1ix2 + -3i2 + -1i2x + -9x + -3x2 + x3) = 0

Combine like terms: -3ix + 3ix = 0
(27 + 0 + -1ix2 + 1ix2 + -3i2 + -1i2x + -9x + -3x2 + x3) = 0
(27 + -1ix2 + 1ix2 + -3i2 + -1i2x + -9x + -3x2 + x3) = 0

Combine like terms: -1ix2 + 1ix2 = 0
(27 + 0 + -3i2 + -1i2x + -9x + -3x2 + x3) = 0
(27 + -3i2 + -1i2x + -9x + -3x2 + x3) = 0

Solving
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = 0

Solving for variable 'i'.

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

Add '-27' to each side of the equation.
27 + -3i2 + -1i2x + -9x + -3x2 + -27 + x3 = 0 + -27

Reorder the terms:
27 + -27 + -3i2 + -1i2x + -9x + -3x2 + x3 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -3i2 + -1i2x + -9x + -3x2 + x3 = 0 + -27
-3i2 + -1i2x + -9x + -3x2 + x3 = 0 + -27

Combine like terms: 0 + -27 = -27
-3i2 + -1i2x + -9x + -3x2 + x3 = -27

Add '9x' to each side of the equation.
-3i2 + -1i2x + -9x + -3x2 + 9x + x3 = -27 + 9x

Reorder the terms:
-3i2 + -1i2x + -9x + 9x + -3x2 + x3 = -27 + 9x

Combine like terms: -9x + 9x = 0
-3i2 + -1i2x + 0 + -3x2 + x3 = -27 + 9x
-3i2 + -1i2x + -3x2 + x3 = -27 + 9x

Add '3x2' to each side of the equation.
-3i2 + -1i2x + -3x2 + 3x2 + x3 = -27 + 9x + 3x2

Combine like terms: -3x2 + 3x2 = 0
-3i2 + -1i2x + 0 + x3 = -27 + 9x + 3x2
-3i2 + -1i2x + x3 = -27 + 9x + 3x2

Add '-1x3' to each side of the equation.
-3i2 + -1i2x + x3 + -1x3 = -27 + 9x + 3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-3i2 + -1i2x + 0 = -27 + 9x + 3x2 + -1x3
-3i2 + -1i2x = -27 + 9x + 3x2 + -1x3

Reorder the terms:
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = -27 + 9x + 3x2 + -1x3 + 27 + -9x + -3x2 + x3

Reorder the terms:
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = -27 + 27 + 9x + -9x + 3x2 + -3x2 + -1x3 + x3

Combine like terms: -27 + 27 = 0
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = 0 + 9x + -9x + 3x2 + -3x2 + -1x3 + x3
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = 9x + -9x + 3x2 + -3x2 + -1x3 + x3

Combine like terms: 9x + -9x = 0
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = 0 + 3x2 + -3x2 + -1x3 + x3
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = 3x2 + -3x2 + -1x3 + x3

Combine like terms: 3x2 + -3x2 = 0
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = 0 + -1x3 + x3
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
27 + -3i2 + -1i2x + -9x + -3x2 + x3 = 0

The solution to this equation could not be determined.

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