(x+4i)(x-4i)(x-(1-i))(x+(1-i))(x+4)=x

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Solution for (x+4i)(x-4i)(x-(1-i))(x+(1-i))(x+4)=x equation: 


Simplifying
(x + 4i)(x + -4i)(x + -1(1 + -1i))(x + (1 + -1i))(x + 4) = x

Reorder the terms:
(4i + x)(x + -4i)(x + -1(1 + -1i))(x + (1 + -1i))(x + 4) = x

Reorder the terms:
(4i + x)(-4i + x)(x + -1(1 + -1i))(x + (1 + -1i))(x + 4) = x
(4i + x)(-4i + x)(x + (1 * -1 + -1i * -1))(x + (1 + -1i))(x + 4) = x
(4i + x)(-4i + x)(x + (-1 + 1i))(x + (1 + -1i))(x + 4) = x

Reorder the terms:
(4i + x)(-4i + x)(-1 + 1i + x)(x + (1 + -1i))(x + 4) = x

Remove parenthesis around (1 + -1i)
(4i + x)(-4i + x)(-1 + 1i + x)(x + 1 + -1i)(x + 4) = x

Reorder the terms:
(4i + x)(-4i + x)(-1 + 1i + x)(1 + -1i + x)(x + 4) = x

Reorder the terms:
(4i + x)(-4i + x)(-1 + 1i + x)(1 + -1i + x)(4 + x) = x

Multiply (4i + x) * (-4i + x)
(4i * (-4i + x) + x(-4i + x))(-1 + 1i + x)(1 + -1i + x)(4 + x) = x
((-4i * 4i + x * 4i) + x(-4i + x))(-1 + 1i + x)(1 + -1i + x)(4 + x) = x

Reorder the terms:
((4ix + -16i2) + x(-4i + x))(-1 + 1i + x)(1 + -1i + x)(4 + x) = x
((4ix + -16i2) + x(-4i + x))(-1 + 1i + x)(1 + -1i + x)(4 + x) = x
(4ix + -16i2 + (-4i * x + x * x))(-1 + 1i + x)(1 + -1i + x)(4 + x) = x
(4ix + -16i2 + (-4ix + x2))(-1 + 1i + x)(1 + -1i + x)(4 + x) = x

Reorder the terms:
(4ix + -4ix + -16i2 + x2)(-1 + 1i + x)(1 + -1i + x)(4 + x) = x

Combine like terms: 4ix + -4ix = 0
(0 + -16i2 + x2)(-1 + 1i + x)(1 + -1i + x)(4 + x) = x
(-16i2 + x2)(-1 + 1i + x)(1 + -1i + x)(4 + x) = x

Multiply (-16i2 + x2) * (-1 + 1i + x)
(-16i2 * (-1 + 1i + x) + x2(-1 + 1i + x))(1 + -1i + x)(4 + x) = x
((-1 * -16i2 + 1i * -16i2 + x * -16i2) + x2(-1 + 1i + x))(1 + -1i + x)(4 + x) = x

Reorder the terms:
((16i2 + -16i2x + -16i3) + x2(-1 + 1i + x))(1 + -1i + x)(4 + x) = x
((16i2 + -16i2x + -16i3) + x2(-1 + 1i + x))(1 + -1i + x)(4 + x) = x
(16i2 + -16i2x + -16i3 + (-1 * x2 + 1i * x2 + x * x2))(1 + -1i + x)(4 + x) = x

Reorder the terms:
(16i2 + -16i2x + -16i3 + (1ix2 + -1x2 + x3))(1 + -1i + x)(4 + x) = x
(16i2 + -16i2x + -16i3 + (1ix2 + -1x2 + x3))(1 + -1i + x)(4 + x) = x

Reorder the terms:
(1ix2 + 16i2 + -16i2x + -16i3 + -1x2 + x3)(1 + -1i + x)(4 + x) = x
(1ix2 + 16i2 + -16i2x + -16i3 + -1x2 + x3)(1 + -1i + x)(4 + x) = x

Multiply (1ix2 + 16i2 + -16i2x + -16i3 + -1x2 + x3) * (1 + -1i + x)
(1ix2 * (1 + -1i + x) + 16i2 * (1 + -1i + x) + -16i2x * (1 + -1i + x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x
((1 * 1ix2 + -1i * 1ix2 + x * 1ix2) + 16i2 * (1 + -1i + x) + -16i2x * (1 + -1i + x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x

Reorder the terms:
((1ix2 + 1ix3 + -1i2x2) + 16i2 * (1 + -1i + x) + -16i2x * (1 + -1i + x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x
((1ix2 + 1ix3 + -1i2x2) + 16i2 * (1 + -1i + x) + -16i2x * (1 + -1i + x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + (1 * 16i2 + -1i * 16i2 + x * 16i2) + -16i2x * (1 + -1i + x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x

Reorder the terms:
(1ix2 + 1ix3 + -1i2x2 + (16i2 + 16i2x + -16i3) + -16i2x * (1 + -1i + x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + (16i2 + 16i2x + -16i3) + -16i2x * (1 + -1i + x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + (1 * -16i2x + -1i * -16i2x + x * -16i2x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x

Reorder the terms:
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + (-16i2x + -16i2x2 + 16i3x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + (-16i2x + -16i2x2 + 16i3x) + -16i3 * (1 + -1i + x) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + -16i2x + -16i2x2 + 16i3x + (1 * -16i3 + -1i * -16i3 + x * -16i3) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x

Reorder the terms:
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + -16i2x + -16i2x2 + 16i3x + (-16i3 + -16i3x + 16i4) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + -16i2x + -16i2x2 + 16i3x + (-16i3 + -16i3x + 16i4) + -1x2 * (1 + -1i + x) + x3(1 + -1i + x))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + -16i2x + -16i2x2 + 16i3x + -16i3 + -16i3x + 16i4 + (1 * -1x2 + -1i * -1x2 + x * -1x2) + x3(1 + -1i + x))(4 + x) = x

Reorder the terms:
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + -16i2x + -16i2x2 + 16i3x + -16i3 + -16i3x + 16i4 + (1ix2 + -1x2 + -1x3) + x3(1 + -1i + x))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + -16i2x + -16i2x2 + 16i3x + -16i3 + -16i3x + 16i4 + (1ix2 + -1x2 + -1x3) + x3(1 + -1i + x))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + -16i2x + -16i2x2 + 16i3x + -16i3 + -16i3x + 16i4 + 1ix2 + -1x2 + -1x3 + (1 * x3 + -1i * x3 + x * x3))(4 + x) = x

Reorder the terms:
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + -16i2x + -16i2x2 + 16i3x + -16i3 + -16i3x + 16i4 + 1ix2 + -1x2 + -1x3 + (-1ix3 + 1x3 + x4))(4 + x) = x
(1ix2 + 1ix3 + -1i2x2 + 16i2 + 16i2x + -16i3 + -16i2x + -16i2x2 + 16i3x + -16i3 + -16i3x + 16i4 + 1ix2 + -1x2 + -1x3 + (-1ix3 + 1x3 + x4))(4 + x) = x

Reorder the terms:
(1ix2 + 1ix2 + 1ix3 + -1ix3 + 16i2 + 16i2x + -16i2x + -1i2x2 + -16i2x2 + -16i3 + -16i3 + 16i3x + -16i3x + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x

Combine like terms: 1ix2 + 1ix2 = 2ix2
(2ix2 + 1ix3 + -1ix3 + 16i2 + 16i2x + -16i2x + -1i2x2 + -16i2x2 + -16i3 + -16i3 + 16i3x + -16i3x + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x

Combine like terms: 1ix3 + -1ix3 = 0
(2ix2 + 0 + 16i2 + 16i2x + -16i2x + -1i2x2 + -16i2x2 + -16i3 + -16i3 + 16i3x + -16i3x + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x
(2ix2 + 16i2 + 16i2x + -16i2x + -1i2x2 + -16i2x2 + -16i3 + -16i3 + 16i3x + -16i3x + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x

Combine like terms: 16i2x + -16i2x = 0
(2ix2 + 16i2 + 0 + -1i2x2 + -16i2x2 + -16i3 + -16i3 + 16i3x + -16i3x + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x
(2ix2 + 16i2 + -1i2x2 + -16i2x2 + -16i3 + -16i3 + 16i3x + -16i3x + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x

Combine like terms: -1i2x2 + -16i2x2 = -17i2x2
(2ix2 + 16i2 + -17i2x2 + -16i3 + -16i3 + 16i3x + -16i3x + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x

Combine like terms: -16i3 + -16i3 = -32i3
(2ix2 + 16i2 + -17i2x2 + -32i3 + 16i3x + -16i3x + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x

Combine like terms: 16i3x + -16i3x = 0
(2ix2 + 16i2 + -17i2x2 + -32i3 + 0 + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x
(2ix2 + 16i2 + -17i2x2 + -32i3 + 16i4 + -1x2 + -1x3 + 1x3 + x4)(4 + x) = x

Combine like terms: -1x3 + 1x3 = 0
(2ix2 + 16i2 + -17i2x2 + -32i3 + 16i4 + -1x2 + 0 + x4)(4 + x) = x
(2ix2 + 16i2 + -17i2x2 + -32i3 + 16i4 + -1x2 + x4)(4 + x) = x

Multiply (2ix2 + 16i2 + -17i2x2 + -32i3 + 16i4 + -1x2 + x4) * (4 + x)
(2ix2 * (4 + x) + 16i2 * (4 + x) + -17i2x2 * (4 + x) + -32i3 * (4 + x) + 16i4 * (4 + x) + -1x2 * (4 + x) + x4(4 + x)) = x
((4 * 2ix2 + x * 2ix2) + 16i2 * (4 + x) + -17i2x2 * (4 + x) + -32i3 * (4 + x) + 16i4 * (4 + x) + -1x2 * (4 + x) + x4(4 + x)) = x
((8ix2 + 2ix3) + 16i2 * (4 + x) + -17i2x2 * (4 + x) + -32i3 * (4 + x) + 16i4 * (4 + x) + -1x2 * (4 + x) + x4(4 + x)) = x
(8ix2 + 2ix3 + (4 * 16i2 + x * 16i2) + -17i2x2 * (4 + x) + -32i3 * (4 + x) + 16i4 * (4 + x) + -1x2 * (4 + x) + x4(4 + x)) = x
(8ix2 + 2ix3 + (64i2 + 16i2x) + -17i2x2 * (4 + x) + -32i3 * (4 + x) + 16i4 * (4 + x) + -1x2 * (4 + x) + x4(4 + x)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + (4 * -17i2x2 + x * -17i2x2) + -32i3 * (4 + x) + 16i4 * (4 + x) + -1x2 * (4 + x) + x4(4 + x)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + (-68i2x2 + -17i2x3) + -32i3 * (4 + x) + 16i4 * (4 + x) + -1x2 * (4 + x) + x4(4 + x)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + (4 * -32i3 + x * -32i3) + 16i4 * (4 + x) + -1x2 * (4 + x) + x4(4 + x)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + (-128i3 + -32i3x) + 16i4 * (4 + x) + -1x2 * (4 + x) + x4(4 + x)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + (4 * 16i4 + x * 16i4) + -1x2 * (4 + x) + x4(4 + x)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + (64i4 + 16i4x) + -1x2 * (4 + x) + x4(4 + x)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + 64i4 + 16i4x + (4 * -1x2 + x * -1x2) + x4(4 + x)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + 64i4 + 16i4x + (-4x2 + -1x3) + x4(4 + x)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + 64i4 + 16i4x + -4x2 + -1x3 + (4 * x4 + x * x4)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + 64i4 + 16i4x + -4x2 + -1x3 + (4x4 + x5)) = x
(8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + 64i4 + 16i4x + -4x2 + -1x3 + 4x4 + x5) = x

Solving
8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + 64i4 + 16i4x + -4x2 + -1x3 + 4x4 + x5 = x

Solving for variable 'i'.

Reorder the terms:
8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + 64i4 + 16i4x + -1x + -4x2 + -1x3 + 4x4 + x5 = x + -1x

Combine like terms: x + -1x = 0
8ix2 + 2ix3 + 64i2 + 16i2x + -68i2x2 + -17i2x3 + -128i3 + -32i3x + 64i4 + 16i4x + -1x + -4x2 + -1x3 + 4x4 + x5 = 0

The solution to this equation could not be determined.

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