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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Reorder the terms:
((2ix2 + -2ix3 + -4i2x2) + 1i2 * (-1 + 2i + x) + -1i2x * (-1 + 2i + x) + 2i3 * (-1 + 2i + x) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0
((2ix2 + -2ix3 + -4i2x2) + 1i2 * (-1 + 2i + x) + -1i2x * (-1 + 2i + x) + 2i3 * (-1 + 2i + x) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + (-1 * 1i2 + 2i * 1i2 + x * 1i2) + -1i2x * (-1 + 2i + x) + 2i3 * (-1 + 2i + x) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0

Reorder the terms:
(2ix2 + -2ix3 + -4i2x2 + (-1i2 + 1i2x + 2i3) + -1i2x * (-1 + 2i + x) + 2i3 * (-1 + 2i + x) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + (-1i2 + 1i2x + 2i3) + -1i2x * (-1 + 2i + x) + 2i3 * (-1 + 2i + x) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + (-1 * -1i2x + 2i * -1i2x + x * -1i2x) + 2i3 * (-1 + 2i + x) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0

Reorder the terms:
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + (1i2x + -1i2x2 + -2i3x) + 2i3 * (-1 + 2i + x) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + (1i2x + -1i2x2 + -2i3x) + 2i3 * (-1 + 2i + x) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + 1i2x + -1i2x2 + -2i3x + (-1 * 2i3 + 2i * 2i3 + x * 2i3) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0

Reorder the terms:
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + 1i2x + -1i2x2 + -2i3x + (-2i3 + 2i3x + 4i4) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + 1i2x + -1i2x2 + -2i3x + (-2i3 + 2i3x + 4i4) + -1x2 * (-1 + 2i + x) + x3(-1 + 2i + x))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + 1i2x + -1i2x2 + -2i3x + -2i3 + 2i3x + 4i4 + (-1 * -1x2 + 2i * -1x2 + x * -1x2) + x3(-1 + 2i + x))(1 + x) = 0

Reorder the terms:
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + 1i2x + -1i2x2 + -2i3x + -2i3 + 2i3x + 4i4 + (-2ix2 + 1x2 + -1x3) + x3(-1 + 2i + x))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + 1i2x + -1i2x2 + -2i3x + -2i3 + 2i3x + 4i4 + (-2ix2 + 1x2 + -1x3) + x3(-1 + 2i + x))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + 1i2x + -1i2x2 + -2i3x + -2i3 + 2i3x + 4i4 + -2ix2 + 1x2 + -1x3 + (-1 * x3 + 2i * x3 + x * x3))(1 + x) = 0

Reorder the terms:
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + 1i2x + -1i2x2 + -2i3x + -2i3 + 2i3x + 4i4 + -2ix2 + 1x2 + -1x3 + (2ix3 + -1x3 + x4))(1 + x) = 0
(2ix2 + -2ix3 + -4i2x2 + -1i2 + 1i2x + 2i3 + 1i2x + -1i2x2 + -2i3x + -2i3 + 2i3x + 4i4 + -2ix2 + 1x2 + -1x3 + (2ix3 + -1x3 + x4))(1 + x) = 0

Reorder the terms:
(2ix2 + -2ix2 + -2ix3 + 2ix3 + -1i2 + 1i2x + 1i2x + -4i2x2 + -1i2x2 + 2i3 + -2i3 + -2i3x + 2i3x + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0

Combine like terms: 2ix2 + -2ix2 = 0
(0 + -2ix3 + 2ix3 + -1i2 + 1i2x + 1i2x + -4i2x2 + -1i2x2 + 2i3 + -2i3 + -2i3x + 2i3x + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0
(-2ix3 + 2ix3 + -1i2 + 1i2x + 1i2x + -4i2x2 + -1i2x2 + 2i3 + -2i3 + -2i3x + 2i3x + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0

Combine like terms: -2ix3 + 2ix3 = 0
(0 + -1i2 + 1i2x + 1i2x + -4i2x2 + -1i2x2 + 2i3 + -2i3 + -2i3x + 2i3x + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0
(-1i2 + 1i2x + 1i2x + -4i2x2 + -1i2x2 + 2i3 + -2i3 + -2i3x + 2i3x + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0

Combine like terms: 1i2x + 1i2x = 2i2x
(-1i2 + 2i2x + -4i2x2 + -1i2x2 + 2i3 + -2i3 + -2i3x + 2i3x + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0

Combine like terms: -4i2x2 + -1i2x2 = -5i2x2
(-1i2 + 2i2x + -5i2x2 + 2i3 + -2i3 + -2i3x + 2i3x + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0

Combine like terms: 2i3 + -2i3 = 0
(-1i2 + 2i2x + -5i2x2 + 0 + -2i3x + 2i3x + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0
(-1i2 + 2i2x + -5i2x2 + -2i3x + 2i3x + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0

Combine like terms: -2i3x + 2i3x = 0
(-1i2 + 2i2x + -5i2x2 + 0 + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0
(-1i2 + 2i2x + -5i2x2 + 4i4 + 1x2 + -1x3 + -1x3 + x4)(1 + x) = 0

Combine like terms: -1x3 + -1x3 = -2x3
(-1i2 + 2i2x + -5i2x2 + 4i4 + 1x2 + -2x3 + x4)(1 + x) = 0

Multiply (-1i2 + 2i2x + -5i2x2 + 4i4 + 1x2 + -2x3 + x4) * (1 + x)
(-1i2 * (1 + x) + 2i2x * (1 + x) + -5i2x2 * (1 + x) + 4i4 * (1 + x) + 1x2 * (1 + x) + -2x3 * (1 + x) + x4(1 + x)) = 0
((1 * -1i2 + x * -1i2) + 2i2x * (1 + x) + -5i2x2 * (1 + x) + 4i4 * (1 + x) + 1x2 * (1 + x) + -2x3 * (1 + x) + x4(1 + x)) = 0
((-1i2 + -1i2x) + 2i2x * (1 + x) + -5i2x2 * (1 + x) + 4i4 * (1 + x) + 1x2 * (1 + x) + -2x3 * (1 + x) + x4(1 + x)) = 0
(-1i2 + -1i2x + (1 * 2i2x + x * 2i2x) + -5i2x2 * (1 + x) + 4i4 * (1 + x) + 1x2 * (1 + x) + -2x3 * (1 + x) + x4(1 + x)) = 0
(-1i2 + -1i2x + (2i2x + 2i2x2) + -5i2x2 * (1 + x) + 4i4 * (1 + x) + 1x2 * (1 + x) + -2x3 * (1 + x) + x4(1 + x)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + (1 * -5i2x2 + x * -5i2x2) + 4i4 * (1 + x) + 1x2 * (1 + x) + -2x3 * (1 + x) + x4(1 + x)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + (-5i2x2 + -5i2x3) + 4i4 * (1 + x) + 1x2 * (1 + x) + -2x3 * (1 + x) + x4(1 + x)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + -5i2x2 + -5i2x3 + (1 * 4i4 + x * 4i4) + 1x2 * (1 + x) + -2x3 * (1 + x) + x4(1 + x)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + -5i2x2 + -5i2x3 + (4i4 + 4i4x) + 1x2 * (1 + x) + -2x3 * (1 + x) + x4(1 + x)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + -5i2x2 + -5i2x3 + 4i4 + 4i4x + (1 * 1x2 + x * 1x2) + -2x3 * (1 + x) + x4(1 + x)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + -5i2x2 + -5i2x3 + 4i4 + 4i4x + (1x2 + 1x3) + -2x3 * (1 + x) + x4(1 + x)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + -5i2x2 + -5i2x3 + 4i4 + 4i4x + 1x2 + 1x3 + (1 * -2x3 + x * -2x3) + x4(1 + x)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + -5i2x2 + -5i2x3 + 4i4 + 4i4x + 1x2 + 1x3 + (-2x3 + -2x4) + x4(1 + x)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + -5i2x2 + -5i2x3 + 4i4 + 4i4x + 1x2 + 1x3 + -2x3 + -2x4 + (1 * x4 + x * x4)) = 0
(-1i2 + -1i2x + 2i2x + 2i2x2 + -5i2x2 + -5i2x3 + 4i4 + 4i4x + 1x2 + 1x3 + -2x3 + -2x4 + (1x4 + x5)) = 0

Combine like terms: -1i2x + 2i2x = 1i2x
(-1i2 + 1i2x + 2i2x2 + -5i2x2 + -5i2x3 + 4i4 + 4i4x + 1x2 + 1x3 + -2x3 + -2x4 + 1x4 + x5) = 0

Combine like terms: 2i2x2 + -5i2x2 = -3i2x2
(-1i2 + 1i2x + -3i2x2 + -5i2x3 + 4i4 + 4i4x + 1x2 + 1x3 + -2x3 + -2x4 + 1x4 + x5) = 0

Combine like terms: 1x3 + -2x3 = -1x3
(-1i2 + 1i2x + -3i2x2 + -5i2x3 + 4i4 + 4i4x + 1x2 + -1x3 + -2x4 + 1x4 + x5) = 0

Combine like terms: -2x4 + 1x4 = -1x4
(-1i2 + 1i2x + -3i2x2 + -5i2x3 + 4i4 + 4i4x + 1x2 + -1x3 + -1x4 + x5) = 0

Solving
-1i2 + 1i2x + -3i2x2 + -5i2x3 + 4i4 + 4i4x + 1x2 + -1x3 + -1x4 + x5 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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