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

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Solution for 0=(x-1)(x-(3+i))(x-(3-i)) equation:


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

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

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

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

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

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

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

Combine like terms: -1x + -3x = -4x
0 = (3 + 1i + -1ix + -4x + x2)(-3 + 1i + x)

Multiply (3 + 1i + -1ix + -4x + x2) * (-3 + 1i + x)
0 = (3(-3 + 1i + x) + 1i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + -4x * (-3 + 1i + x) + x2(-3 + 1i + x))
0 = ((-3 * 3 + 1i * 3 + x * 3) + 1i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + -4x * (-3 + 1i + x) + x2(-3 + 1i + x))
0 = ((-9 + 3i + 3x) + 1i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + -4x * (-3 + 1i + x) + x2(-3 + 1i + x))
0 = (-9 + 3i + 3x + (-3 * 1i + 1i * 1i + x * 1i) + -1ix * (-3 + 1i + x) + -4x * (-3 + 1i + x) + x2(-3 + 1i + x))

Reorder the terms:
0 = (-9 + 3i + 3x + (-3i + 1ix + 1i2) + -1ix * (-3 + 1i + x) + -4x * (-3 + 1i + x) + x2(-3 + 1i + x))
0 = (-9 + 3i + 3x + (-3i + 1ix + 1i2) + -1ix * (-3 + 1i + x) + -4x * (-3 + 1i + x) + x2(-3 + 1i + x))
0 = (-9 + 3i + 3x + -3i + 1ix + 1i2 + (-3 * -1ix + 1i * -1ix + x * -1ix) + -4x * (-3 + 1i + x) + x2(-3 + 1i + x))

Reorder the terms:
0 = (-9 + 3i + 3x + -3i + 1ix + 1i2 + (3ix + -1ix2 + -1i2x) + -4x * (-3 + 1i + x) + x2(-3 + 1i + x))
0 = (-9 + 3i + 3x + -3i + 1ix + 1i2 + (3ix + -1ix2 + -1i2x) + -4x * (-3 + 1i + x) + x2(-3 + 1i + x))
0 = (-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + (-3 * -4x + 1i * -4x + x * -4x) + x2(-3 + 1i + x))

Reorder the terms:
0 = (-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + (-4ix + 12x + -4x2) + x2(-3 + 1i + x))
0 = (-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + (-4ix + 12x + -4x2) + x2(-3 + 1i + x))
0 = (-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + -4ix + 12x + -4x2 + (-3 * x2 + 1i * x2 + x * x2))

Reorder the terms:
0 = (-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + -4ix + 12x + -4x2 + (1ix2 + -3x2 + x3))
0 = (-9 + 3i + 3x + -3i + 1ix + 1i2 + 3ix + -1ix2 + -1i2x + -4ix + 12x + -4x2 + (1ix2 + -3x2 + x3))

Reorder the terms:
0 = (-9 + 3i + -3i + 1ix + 3ix + -4ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3)

Combine like terms: 3i + -3i = 0
0 = (-9 + 0 + 1ix + 3ix + -4ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3)
0 = (-9 + 1ix + 3ix + -4ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3)

Combine like terms: 1ix + 3ix = 4ix
0 = (-9 + 4ix + -4ix + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3)

Combine like terms: 4ix + -4ix = 0
0 = (-9 + 0 + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3)
0 = (-9 + -1ix2 + 1ix2 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3)

Combine like terms: -1ix2 + 1ix2 = 0
0 = (-9 + 0 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3)
0 = (-9 + 1i2 + -1i2x + 3x + 12x + -4x2 + -3x2 + x3)

Combine like terms: 3x + 12x = 15x
0 = (-9 + 1i2 + -1i2x + 15x + -4x2 + -3x2 + x3)

Combine like terms: -4x2 + -3x2 = -7x2
0 = (-9 + 1i2 + -1i2x + 15x + -7x2 + x3)

Solving
0 = -9 + 1i2 + -1i2x + 15x + -7x2 + x3

Solving for variable 'i'.

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

Add '-1i2' to each side of the equation.
0 + -1i2 = -9 + 1i2 + -1i2x + 15x + -7x2 + -1i2 + x3
Remove the zero:
-1i2 = -9 + 1i2 + -1i2x + 15x + -7x2 + -1i2 + x3

Reorder the terms:
-1i2 = -9 + 1i2 + -1i2 + -1i2x + 15x + -7x2 + x3

Combine like terms: 1i2 + -1i2 = 0
-1i2 = -9 + 0 + -1i2x + 15x + -7x2 + x3
-1i2 = -9 + -1i2x + 15x + -7x2 + x3

Add 'i2x' to each side of the equation.
-1i2 + i2x = -9 + -1i2x + 15x + -7x2 + i2x + x3

Reorder the terms:
-1i2 + i2x = -9 + -1i2x + i2x + 15x + -7x2 + x3

Combine like terms: -1i2x + i2x = 0
-1i2 + i2x = -9 + 0 + 15x + -7x2 + x3
-1i2 + i2x = -9 + 15x + -7x2 + x3

Reorder the terms:
9 + -1i2 + i2x + -15x + 7x2 + -1x3 = -9 + 15x + -7x2 + x3 + 9 + -15x + 7x2 + -1x3

Reorder the terms:
9 + -1i2 + i2x + -15x + 7x2 + -1x3 = -9 + 9 + 15x + -15x + -7x2 + 7x2 + x3 + -1x3

Combine like terms: -9 + 9 = 0
9 + -1i2 + i2x + -15x + 7x2 + -1x3 = 0 + 15x + -15x + -7x2 + 7x2 + x3 + -1x3
9 + -1i2 + i2x + -15x + 7x2 + -1x3 = 15x + -15x + -7x2 + 7x2 + x3 + -1x3

Combine like terms: 15x + -15x = 0
9 + -1i2 + i2x + -15x + 7x2 + -1x3 = 0 + -7x2 + 7x2 + x3 + -1x3
9 + -1i2 + i2x + -15x + 7x2 + -1x3 = -7x2 + 7x2 + x3 + -1x3

Combine like terms: -7x2 + 7x2 = 0
9 + -1i2 + i2x + -15x + 7x2 + -1x3 = 0 + x3 + -1x3
9 + -1i2 + i2x + -15x + 7x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
9 + -1i2 + i2x + -15x + 7x2 + -1x3 = 0

The solution to this equation could not be determined.

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