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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
3 + -3i2 + -1i2x + -5x + 1x2 + x3 = 0

Solving for variable 'i'.

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

Add '-3' to each side of the equation.
3 + -3i2 + -1i2x + -5x + 1x2 + -3 + x3 = 0 + -3

Reorder the terms:
3 + -3 + -3i2 + -1i2x + -5x + 1x2 + x3 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -3i2 + -1i2x + -5x + 1x2 + x3 = 0 + -3
-3i2 + -1i2x + -5x + 1x2 + x3 = 0 + -3

Combine like terms: 0 + -3 = -3
-3i2 + -1i2x + -5x + 1x2 + x3 = -3

Add '5x' to each side of the equation.
-3i2 + -1i2x + -5x + 1x2 + 5x + x3 = -3 + 5x

Reorder the terms:
-3i2 + -1i2x + -5x + 5x + 1x2 + x3 = -3 + 5x

Combine like terms: -5x + 5x = 0
-3i2 + -1i2x + 0 + 1x2 + x3 = -3 + 5x
-3i2 + -1i2x + 1x2 + x3 = -3 + 5x

Add '-1x2' to each side of the equation.
-3i2 + -1i2x + 1x2 + -1x2 + x3 = -3 + 5x + -1x2

Combine like terms: 1x2 + -1x2 = 0
-3i2 + -1i2x + 0 + x3 = -3 + 5x + -1x2
-3i2 + -1i2x + x3 = -3 + 5x + -1x2

Add '-1x3' to each side of the equation.
-3i2 + -1i2x + x3 + -1x3 = -3 + 5x + -1x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-3i2 + -1i2x + 0 = -3 + 5x + -1x2 + -1x3
-3i2 + -1i2x = -3 + 5x + -1x2 + -1x3

Reorder the terms:
3 + -3i2 + -1i2x + -5x + x2 + x3 = -3 + 5x + -1x2 + -1x3 + 3 + -5x + x2 + x3

Reorder the terms:
3 + -3i2 + -1i2x + -5x + x2 + x3 = -3 + 3 + 5x + -5x + -1x2 + x2 + -1x3 + x3

Combine like terms: -3 + 3 = 0
3 + -3i2 + -1i2x + -5x + x2 + x3 = 0 + 5x + -5x + -1x2 + x2 + -1x3 + x3
3 + -3i2 + -1i2x + -5x + x2 + x3 = 5x + -5x + -1x2 + x2 + -1x3 + x3

Combine like terms: 5x + -5x = 0
3 + -3i2 + -1i2x + -5x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3
3 + -3i2 + -1i2x + -5x + x2 + x3 = -1x2 + x2 + -1x3 + x3

Combine like terms: -1x2 + x2 = 0
3 + -3i2 + -1i2x + -5x + x2 + x3 = 0 + -1x3 + x3
3 + -3i2 + -1i2x + -5x + x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
3 + -3i2 + -1i2x + -5x + x2 + x3 = 0

The solution to this equation could not be determined.

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