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

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Solution for (x+1)(x-2)(x-1+i)(x-1-i)=0 equation: 


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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply (2 + -2i + -1ix + ix2 + -1x + -2x2 + x3) * (-1 + -1i + x)
(2(-1 + -1i + x) + -2i * (-1 + -1i + x) + -1ix * (-1 + -1i + x) + ix2(-1 + -1i + x) + -1x * (-1 + -1i + x) + -2x2 * (-1 + -1i + x) + x3(-1 + -1i + x)) = 0
((-1 * 2 + -1i * 2 + x * 2) + -2i * (-1 + -1i + x) + -1ix * (-1 + -1i + x) + ix2(-1 + -1i + x) + -1x * (-1 + -1i + x) + -2x2 * (-1 + -1i + x) + x3(-1 + -1i + x)) = 0
((-2 + -2i + 2x) + -2i * (-1 + -1i + x) + -1ix * (-1 + -1i + x) + ix2(-1 + -1i + x) + -1x * (-1 + -1i + x) + -2x2 * (-1 + -1i + x) + x3(-1 + -1i + x)) = 0
(-2 + -2i + 2x + (-1 * -2i + -1i * -2i + x * -2i) + -1ix * (-1 + -1i + x) + ix2(-1 + -1i + x) + -1x * (-1 + -1i + x) + -2x2 * (-1 + -1i + x) + x3(-1 + -1i + x)) = 0

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

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

Reorder the terms:
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + (-1ix2 + ix3 + -1i2x2) + -1x * (-1 + -1i + x) + -2x2 * (-1 + -1i + x) + x3(-1 + -1i + x)) = 0
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + (-1ix2 + ix3 + -1i2x2) + -1x * (-1 + -1i + x) + -2x2 * (-1 + -1i + x) + x3(-1 + -1i + x)) = 0
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + -1ix2 + ix3 + -1i2x2 + (-1 * -1x + -1i * -1x + x * -1x) + -2x2 * (-1 + -1i + x) + x3(-1 + -1i + x)) = 0

Reorder the terms:
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + -1ix2 + ix3 + -1i2x2 + (1ix + 1x + -1x2) + -2x2 * (-1 + -1i + x) + x3(-1 + -1i + x)) = 0
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + -1ix2 + ix3 + -1i2x2 + (1ix + 1x + -1x2) + -2x2 * (-1 + -1i + x) + x3(-1 + -1i + x)) = 0
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + -1ix2 + ix3 + -1i2x2 + 1ix + 1x + -1x2 + (-1 * -2x2 + -1i * -2x2 + x * -2x2) + x3(-1 + -1i + x)) = 0

Reorder the terms:
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + -1ix2 + ix3 + -1i2x2 + 1ix + 1x + -1x2 + (2ix2 + 2x2 + -2x3) + x3(-1 + -1i + x)) = 0
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + -1ix2 + ix3 + -1i2x2 + 1ix + 1x + -1x2 + (2ix2 + 2x2 + -2x3) + x3(-1 + -1i + x)) = 0
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + -1ix2 + ix3 + -1i2x2 + 1ix + 1x + -1x2 + 2ix2 + 2x2 + -2x3 + (-1 * x3 + -1i * x3 + x * x3)) = 0

Reorder the terms:
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + -1ix2 + ix3 + -1i2x2 + 1ix + 1x + -1x2 + 2ix2 + 2x2 + -2x3 + (-1ix3 + -1x3 + x4)) = 0
(-2 + -2i + 2x + 2i + -2ix + 2i2 + 1ix + -1ix2 + 1i2x + -1ix2 + ix3 + -1i2x2 + 1ix + 1x + -1x2 + 2ix2 + 2x2 + -2x3 + (-1ix3 + -1x3 + x4)) = 0

Reorder the terms:
(-2 + -2i + 2i + -2ix + 1ix + 1ix + -1ix2 + -1ix2 + 2ix2 + ix3 + -1ix3 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0

Combine like terms: -2i + 2i = 0
(-2 + 0 + -2ix + 1ix + 1ix + -1ix2 + -1ix2 + 2ix2 + ix3 + -1ix3 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0
(-2 + -2ix + 1ix + 1ix + -1ix2 + -1ix2 + 2ix2 + ix3 + -1ix3 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0

Combine like terms: -2ix + 1ix = -1ix
(-2 + -1ix + 1ix + -1ix2 + -1ix2 + 2ix2 + ix3 + -1ix3 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0

Combine like terms: -1ix + 1ix = 0
(-2 + 0 + -1ix2 + -1ix2 + 2ix2 + ix3 + -1ix3 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0
(-2 + -1ix2 + -1ix2 + 2ix2 + ix3 + -1ix3 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0

Combine like terms: -1ix2 + -1ix2 = -2ix2
(-2 + -2ix2 + 2ix2 + ix3 + -1ix3 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0

Combine like terms: -2ix2 + 2ix2 = 0
(-2 + 0 + ix3 + -1ix3 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0
(-2 + ix3 + -1ix3 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0

Combine like terms: ix3 + -1ix3 = 0
(-2 + 0 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0
(-2 + 2i2 + 1i2x + -1i2x2 + 2x + 1x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0

Combine like terms: 2x + 1x = 3x
(-2 + 2i2 + 1i2x + -1i2x2 + 3x + -1x2 + 2x2 + -2x3 + -1x3 + x4) = 0

Combine like terms: -1x2 + 2x2 = 1x2
(-2 + 2i2 + 1i2x + -1i2x2 + 3x + 1x2 + -2x3 + -1x3 + x4) = 0

Combine like terms: -2x3 + -1x3 = -3x3
(-2 + 2i2 + 1i2x + -1i2x2 + 3x + 1x2 + -3x3 + x4) = 0

Solving
-2 + 2i2 + 1i2x + -1i2x2 + 3x + 1x2 + -3x3 + x4 = 0

Solving for variable 'i'.

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

Add '2' to each side of the equation.
-2 + 2i2 + 1i2x + -1i2x2 + 3x + 1x2 + -3x3 + 2 + x4 = 0 + 2

Reorder the terms:
-2 + 2 + 2i2 + 1i2x + -1i2x2 + 3x + 1x2 + -3x3 + x4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2i2 + 1i2x + -1i2x2 + 3x + 1x2 + -3x3 + x4 = 0 + 2
2i2 + 1i2x + -1i2x2 + 3x + 1x2 + -3x3 + x4 = 0 + 2

Combine like terms: 0 + 2 = 2
2i2 + 1i2x + -1i2x2 + 3x + 1x2 + -3x3 + x4 = 2

Add '-3x' to each side of the equation.
2i2 + 1i2x + -1i2x2 + 3x + 1x2 + -3x3 + -3x + x4 = 2 + -3x

Reorder the terms:
2i2 + 1i2x + -1i2x2 + 3x + -3x + 1x2 + -3x3 + x4 = 2 + -3x

Combine like terms: 3x + -3x = 0
2i2 + 1i2x + -1i2x2 + 0 + 1x2 + -3x3 + x4 = 2 + -3x
2i2 + 1i2x + -1i2x2 + 1x2 + -3x3 + x4 = 2 + -3x

Add '-1x2' to each side of the equation.
2i2 + 1i2x + -1i2x2 + 1x2 + -3x3 + -1x2 + x4 = 2 + -3x + -1x2

Reorder the terms:
2i2 + 1i2x + -1i2x2 + 1x2 + -1x2 + -3x3 + x4 = 2 + -3x + -1x2

Combine like terms: 1x2 + -1x2 = 0
2i2 + 1i2x + -1i2x2 + 0 + -3x3 + x4 = 2 + -3x + -1x2
2i2 + 1i2x + -1i2x2 + -3x3 + x4 = 2 + -3x + -1x2

Add '3x3' to each side of the equation.
2i2 + 1i2x + -1i2x2 + -3x3 + 3x3 + x4 = 2 + -3x + -1x2 + 3x3

Combine like terms: -3x3 + 3x3 = 0
2i2 + 1i2x + -1i2x2 + 0 + x4 = 2 + -3x + -1x2 + 3x3
2i2 + 1i2x + -1i2x2 + x4 = 2 + -3x + -1x2 + 3x3

Add '-1x4' to each side of the equation.
2i2 + 1i2x + -1i2x2 + x4 + -1x4 = 2 + -3x + -1x2 + 3x3 + -1x4

Combine like terms: x4 + -1x4 = 0
2i2 + 1i2x + -1i2x2 + 0 = 2 + -3x + -1x2 + 3x3 + -1x4
2i2 + 1i2x + -1i2x2 = 2 + -3x + -1x2 + 3x3 + -1x4

Reorder the terms:
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = 2 + -3x + -1x2 + 3x3 + -1x4 + -2 + 3x + x2 + -3x3 + x4

Reorder the terms:
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = 2 + -2 + -3x + 3x + -1x2 + x2 + 3x3 + -3x3 + -1x4 + x4

Combine like terms: 2 + -2 = 0
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = 0 + -3x + 3x + -1x2 + x2 + 3x3 + -3x3 + -1x4 + x4
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = -3x + 3x + -1x2 + x2 + 3x3 + -3x3 + -1x4 + x4

Combine like terms: -3x + 3x = 0
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = 0 + -1x2 + x2 + 3x3 + -3x3 + -1x4 + x4
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = -1x2 + x2 + 3x3 + -3x3 + -1x4 + x4

Combine like terms: -1x2 + x2 = 0
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = 0 + 3x3 + -3x3 + -1x4 + x4
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = 3x3 + -3x3 + -1x4 + x4

Combine like terms: 3x3 + -3x3 = 0
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = 0 + -1x4 + x4
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
-2 + 2i2 + 1i2x + -1i2x2 + 3x + x2 + -3x3 + x4 = 0

The solution to this equation could not be determined.

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