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

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


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

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

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

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

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

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

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

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

Multiply (-2ix + 1i2 + x2) * (-1i + x)
(-2ix * (-1i + x) + 1i2 * (-1i + x) + x2(-1i + x)) + (x + i)(x + i)(x + i) = 0
((-1i * -2ix + x * -2ix) + 1i2 * (-1i + x) + x2(-1i + x)) + (x + i)(x + i)(x + i) = 0

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

Reorder the terms:
(-2ix2 + 2i2x + (1i2x + -1i3) + x2(-1i + x)) + (x + i)(x + i)(x + i) = 0
(-2ix2 + 2i2x + (1i2x + -1i3) + x2(-1i + x)) + (x + i)(x + i)(x + i) = 0
(-2ix2 + 2i2x + 1i2x + -1i3 + (-1i * x2 + x * x2)) + (x + i)(x + i)(x + i) = 0
(-2ix2 + 2i2x + 1i2x + -1i3 + (-1ix2 + x3)) + (x + i)(x + i)(x + i) = 0

Reorder the terms:
(-2ix2 + -1ix2 + 2i2x + 1i2x + -1i3 + x3) + (x + i)(x + i)(x + i) = 0

Combine like terms: -2ix2 + -1ix2 = -3ix2
(-3ix2 + 2i2x + 1i2x + -1i3 + x3) + (x + i)(x + i)(x + i) = 0

Combine like terms: 2i2x + 1i2x = 3i2x
(-3ix2 + 3i2x + -1i3 + x3) + (x + i)(x + i)(x + i) = 0

Reorder the terms:
-3ix2 + 3i2x + -1i3 + x3 + (i + x)(x + i)(x + i) = 0

Reorder the terms:
-3ix2 + 3i2x + -1i3 + x3 + (i + x)(i + x)(x + i) = 0

Reorder the terms:
-3ix2 + 3i2x + -1i3 + x3 + (i + x)(i + x)(i + x) = 0

Multiply (i + x) * (i + x)
-3ix2 + 3i2x + -1i3 + x3 + (i(i + x) + x(i + x))(i + x) = 0
-3ix2 + 3i2x + -1i3 + x3 + ((i * i + x * i) + x(i + x))(i + x) = 0

Reorder the terms:
-3ix2 + 3i2x + -1i3 + x3 + ((ix + i2) + x(i + x))(i + x) = 0
-3ix2 + 3i2x + -1i3 + x3 + ((ix + i2) + x(i + x))(i + x) = 0
-3ix2 + 3i2x + -1i3 + x3 + (ix + i2 + (i * x + x * x))(i + x) = 0
-3ix2 + 3i2x + -1i3 + x3 + (ix + i2 + (ix + x2))(i + x) = 0

Reorder the terms:
-3ix2 + 3i2x + -1i3 + x3 + (ix + ix + i2 + x2)(i + x) = 0

Combine like terms: ix + ix = 2ix
-3ix2 + 3i2x + -1i3 + x3 + (2ix + i2 + x2)(i + x) = 0

Multiply (2ix + i2 + x2) * (i + x)
-3ix2 + 3i2x + -1i3 + x3 + (2ix * (i + x) + i2(i + x) + x2(i + x)) = 0
-3ix2 + 3i2x + -1i3 + x3 + ((i * 2ix + x * 2ix) + i2(i + x) + x2(i + x)) = 0

Reorder the terms:
-3ix2 + 3i2x + -1i3 + x3 + ((2ix2 + 2i2x) + i2(i + x) + x2(i + x)) = 0
-3ix2 + 3i2x + -1i3 + x3 + ((2ix2 + 2i2x) + i2(i + x) + x2(i + x)) = 0
-3ix2 + 3i2x + -1i3 + x3 + (2ix2 + 2i2x + (i * i2 + x * i2) + x2(i + x)) = 0

Reorder the terms:
-3ix2 + 3i2x + -1i3 + x3 + (2ix2 + 2i2x + (i2x + i3) + x2(i + x)) = 0
-3ix2 + 3i2x + -1i3 + x3 + (2ix2 + 2i2x + (i2x + i3) + x2(i + x)) = 0
-3ix2 + 3i2x + -1i3 + x3 + (2ix2 + 2i2x + i2x + i3 + (i * x2 + x * x2)) = 0
-3ix2 + 3i2x + -1i3 + x3 + (2ix2 + 2i2x + i2x + i3 + (ix2 + x3)) = 0

Reorder the terms:
-3ix2 + 3i2x + -1i3 + x3 + (2ix2 + ix2 + 2i2x + i2x + i3 + x3) = 0

Combine like terms: 2ix2 + ix2 = 3ix2
-3ix2 + 3i2x + -1i3 + x3 + (3ix2 + 2i2x + i2x + i3 + x3) = 0

Combine like terms: 2i2x + i2x = 3i2x
-3ix2 + 3i2x + -1i3 + x3 + (3ix2 + 3i2x + i3 + x3) = 0

Reorder the terms:
-3ix2 + 3ix2 + 3i2x + 3i2x + -1i3 + i3 + x3 + x3 = 0

Combine like terms: -3ix2 + 3ix2 = 0
0 + 3i2x + 3i2x + -1i3 + i3 + x3 + x3 = 0
3i2x + 3i2x + -1i3 + i3 + x3 + x3 = 0

Combine like terms: 3i2x + 3i2x = 6i2x
6i2x + -1i3 + i3 + x3 + x3 = 0

Combine like terms: -1i3 + i3 = 0
6i2x + 0 + x3 + x3 = 0
6i2x + x3 + x3 = 0

Combine like terms: x3 + x3 = 2x3
6i2x + 2x3 = 0

Solving
6i2x + 2x3 = 0

Solving for variable 'i'.

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

Add '-2x3' to each side of the equation.
6i2x + 2x3 + -2x3 = 0 + -2x3

Combine like terms: 2x3 + -2x3 = 0
6i2x + 0 = 0 + -2x3
6i2x = 0 + -2x3
Remove the zero:
6i2x = -2x3

Divide each side by '6x'.
i2 = -0.3333333333x2

Simplifying
i2 = -0.3333333333x2

Combine like terms: -0.3333333333x2 + 0.3333333333x2 = 0.0000000000
i2 + 0.3333333333x2 = 0.0000000000

The solution to this equation could not be determined.

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