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

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


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

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

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

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

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

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

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

Combine like terms: -3x + -2x = -5x
0 = (6 + -3i + ix + -5x + x2)(-2 + -1i + x)

Multiply (6 + -3i + ix + -5x + x2) * (-2 + -1i + x)
0 = (6(-2 + -1i + x) + -3i * (-2 + -1i + x) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x))
0 = ((-2 * 6 + -1i * 6 + x * 6) + -3i * (-2 + -1i + x) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x))
0 = ((-12 + -6i + 6x) + -3i * (-2 + -1i + x) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x))
0 = (-12 + -6i + 6x + (-2 * -3i + -1i * -3i + x * -3i) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x))

Reorder the terms:
0 = (-12 + -6i + 6x + (6i + -3ix + 3i2) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x))
0 = (-12 + -6i + 6x + (6i + -3ix + 3i2) + ix(-2 + -1i + x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x))
0 = (-12 + -6i + 6x + 6i + -3ix + 3i2 + (-2 * ix + -1i * ix + x * ix) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x))

Reorder the terms:
0 = (-12 + -6i + 6x + 6i + -3ix + 3i2 + (-2ix + ix2 + -1i2x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x))
0 = (-12 + -6i + 6x + 6i + -3ix + 3i2 + (-2ix + ix2 + -1i2x) + -5x * (-2 + -1i + x) + x2(-2 + -1i + x))
0 = (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + (-2 * -5x + -1i * -5x + x * -5x) + x2(-2 + -1i + x))

Reorder the terms:
0 = (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + (5ix + 10x + -5x2) + x2(-2 + -1i + x))
0 = (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + (5ix + 10x + -5x2) + x2(-2 + -1i + x))
0 = (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + 5ix + 10x + -5x2 + (-2 * x2 + -1i * x2 + x * x2))

Reorder the terms:
0 = (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + 5ix + 10x + -5x2 + (-1ix2 + -2x2 + x3))
0 = (-12 + -6i + 6x + 6i + -3ix + 3i2 + -2ix + ix2 + -1i2x + 5ix + 10x + -5x2 + (-1ix2 + -2x2 + x3))

Reorder the terms:
0 = (-12 + -6i + 6i + -3ix + -2ix + 5ix + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3)

Combine like terms: -6i + 6i = 0
0 = (-12 + 0 + -3ix + -2ix + 5ix + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3)
0 = (-12 + -3ix + -2ix + 5ix + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3)

Combine like terms: -3ix + -2ix = -5ix
0 = (-12 + -5ix + 5ix + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3)

Combine like terms: -5ix + 5ix = 0
0 = (-12 + 0 + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3)
0 = (-12 + ix2 + -1ix2 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3)

Combine like terms: ix2 + -1ix2 = 0
0 = (-12 + 0 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3)
0 = (-12 + 3i2 + -1i2x + 6x + 10x + -5x2 + -2x2 + x3)

Combine like terms: 6x + 10x = 16x
0 = (-12 + 3i2 + -1i2x + 16x + -5x2 + -2x2 + x3)

Combine like terms: -5x2 + -2x2 = -7x2
0 = (-12 + 3i2 + -1i2x + 16x + -7x2 + x3)

Solving
0 = -12 + 3i2 + -1i2x + 16x + -7x2 + x3

Solving for variable 'i'.

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

Add '-3i2' to each side of the equation.
0 + -3i2 = -12 + 3i2 + -1i2x + 16x + -7x2 + -3i2 + x3
Remove the zero:
-3i2 = -12 + 3i2 + -1i2x + 16x + -7x2 + -3i2 + x3

Reorder the terms:
-3i2 = -12 + 3i2 + -3i2 + -1i2x + 16x + -7x2 + x3

Combine like terms: 3i2 + -3i2 = 0
-3i2 = -12 + 0 + -1i2x + 16x + -7x2 + x3
-3i2 = -12 + -1i2x + 16x + -7x2 + x3

Add 'i2x' to each side of the equation.
-3i2 + i2x = -12 + -1i2x + 16x + -7x2 + i2x + x3

Reorder the terms:
-3i2 + i2x = -12 + -1i2x + i2x + 16x + -7x2 + x3

Combine like terms: -1i2x + i2x = 0
-3i2 + i2x = -12 + 0 + 16x + -7x2 + x3
-3i2 + i2x = -12 + 16x + -7x2 + x3

Reorder the terms:
12 + -3i2 + i2x + -16x + 7x2 + -1x3 = -12 + 16x + -7x2 + x3 + 12 + -16x + 7x2 + -1x3

Reorder the terms:
12 + -3i2 + i2x + -16x + 7x2 + -1x3 = -12 + 12 + 16x + -16x + -7x2 + 7x2 + x3 + -1x3

Combine like terms: -12 + 12 = 0
12 + -3i2 + i2x + -16x + 7x2 + -1x3 = 0 + 16x + -16x + -7x2 + 7x2 + x3 + -1x3
12 + -3i2 + i2x + -16x + 7x2 + -1x3 = 16x + -16x + -7x2 + 7x2 + x3 + -1x3

Combine like terms: 16x + -16x = 0
12 + -3i2 + i2x + -16x + 7x2 + -1x3 = 0 + -7x2 + 7x2 + x3 + -1x3
12 + -3i2 + i2x + -16x + 7x2 + -1x3 = -7x2 + 7x2 + x3 + -1x3

Combine like terms: -7x2 + 7x2 = 0
12 + -3i2 + i2x + -16x + 7x2 + -1x3 = 0 + x3 + -1x3
12 + -3i2 + i2x + -16x + 7x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
12 + -3i2 + i2x + -16x + 7x2 + -1x3 = 0

The solution to this equation could not be determined.

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