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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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