x(x+i)(x-i)(x+4+i)(x-4-i)=0

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Solution for x(x+i)(x-i)(x+4+i)(x-4-i)=0 equation: 


Simplifying
x(x + i)(x + -1i)(x + 4 + i)(x + -4 + -1i) = 0

Reorder the terms:
x(i + x)(x + -1i)(x + 4 + i)(x + -4 + -1i) = 0

Reorder the terms:
x(i + x)(-1i + x)(x + 4 + i)(x + -4 + -1i) = 0

Reorder the terms:
x(i + x)(-1i + x)(4 + i + x)(x + -4 + -1i) = 0

Reorder the terms:
x(i + x)(-1i + x)(4 + i + x)(-4 + -1i + x) = 0

Multiply (i + x) * (-1i + x)
x(i(-1i + x) + x(-1i + x))(4 + i + x)(-4 + -1i + x) = 0
x((-1i * i + x * i) + x(-1i + x))(4 + i + x)(-4 + -1i + x) = 0

Reorder the terms:
x((ix + -1i2) + x(-1i + x))(4 + i + x)(-4 + -1i + x) = 0
x((ix + -1i2) + x(-1i + x))(4 + i + x)(-4 + -1i + x) = 0
x(ix + -1i2 + (-1i * x + x * x))(4 + i + x)(-4 + -1i + x) = 0
x(ix + -1i2 + (-1ix + x2))(4 + i + x)(-4 + -1i + x) = 0

Reorder the terms:
x(ix + -1ix + -1i2 + x2)(4 + i + x)(-4 + -1i + x) = 0

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

Multiply (-1i2 + x2) * (4 + i + x)
x(-1i2 * (4 + i + x) + x2(4 + i + x))(-4 + -1i + x) = 0
x((4 * -1i2 + i * -1i2 + x * -1i2) + x2(4 + i + x))(-4 + -1i + x) = 0

Reorder the terms:
x((-4i2 + -1i2x + -1i3) + x2(4 + i + x))(-4 + -1i + x) = 0
x((-4i2 + -1i2x + -1i3) + x2(4 + i + x))(-4 + -1i + x) = 0
x(-4i2 + -1i2x + -1i3 + (4 * x2 + i * x2 + x * x2))(-4 + -1i + x) = 0

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

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

Multiply (ix2 + -4i2 + -1i2x + -1i3 + 4x2 + x3) * (-4 + -1i + x)
x(ix2(-4 + -1i + x) + -4i2 * (-4 + -1i + x) + -1i2x * (-4 + -1i + x) + -1i3 * (-4 + -1i + x) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0
x((-4 * ix2 + -1i * ix2 + x * ix2) + -4i2 * (-4 + -1i + x) + -1i2x * (-4 + -1i + x) + -1i3 * (-4 + -1i + x) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0

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

Reorder the terms:
x(-4ix2 + ix3 + -1i2x2 + (16i2 + -4i2x + 4i3) + -1i2x * (-4 + -1i + x) + -1i3 * (-4 + -1i + x) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0
x(-4ix2 + ix3 + -1i2x2 + (16i2 + -4i2x + 4i3) + -1i2x * (-4 + -1i + x) + -1i3 * (-4 + -1i + x) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + (-4 * -1i2x + -1i * -1i2x + x * -1i2x) + -1i3 * (-4 + -1i + x) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0

Reorder the terms:
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + (4i2x + -1i2x2 + 1i3x) + -1i3 * (-4 + -1i + x) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + (4i2x + -1i2x2 + 1i3x) + -1i3 * (-4 + -1i + x) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + 4i2x + -1i2x2 + 1i3x + (-4 * -1i3 + -1i * -1i3 + x * -1i3) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0

Reorder the terms:
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + 4i2x + -1i2x2 + 1i3x + (4i3 + -1i3x + 1i4) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + 4i2x + -1i2x2 + 1i3x + (4i3 + -1i3x + 1i4) + 4x2 * (-4 + -1i + x) + x3(-4 + -1i + x)) = 0
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + 4i2x + -1i2x2 + 1i3x + 4i3 + -1i3x + 1i4 + (-4 * 4x2 + -1i * 4x2 + x * 4x2) + x3(-4 + -1i + x)) = 0

Reorder the terms:
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + 4i2x + -1i2x2 + 1i3x + 4i3 + -1i3x + 1i4 + (-4ix2 + -16x2 + 4x3) + x3(-4 + -1i + x)) = 0
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + 4i2x + -1i2x2 + 1i3x + 4i3 + -1i3x + 1i4 + (-4ix2 + -16x2 + 4x3) + x3(-4 + -1i + x)) = 0
x(-4ix2 + ix3 + -1i2x2 + 16i2 + -4i2x + 4i3 + 4i2x + -1i2x2 + 1i3x + 4i3 + -1i3x + 1i4 + -4ix2 + -16x2 + 4x3 + (-4 * x3 + -1i * x3 + x * x3)) = 0

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

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

Combine like terms: -4ix2 + -4ix2 = -8ix2
x(-8ix2 + ix3 + -1ix3 + 16i2 + -4i2x + 4i2x + -1i2x2 + -1i2x2 + 4i3 + 4i3 + 1i3x + -1i3x + 1i4 + -16x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: ix3 + -1ix3 = 0
x(-8ix2 + 0 + 16i2 + -4i2x + 4i2x + -1i2x2 + -1i2x2 + 4i3 + 4i3 + 1i3x + -1i3x + 1i4 + -16x2 + 4x3 + -4x3 + x4) = 0
x(-8ix2 + 16i2 + -4i2x + 4i2x + -1i2x2 + -1i2x2 + 4i3 + 4i3 + 1i3x + -1i3x + 1i4 + -16x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: -4i2x + 4i2x = 0
x(-8ix2 + 16i2 + 0 + -1i2x2 + -1i2x2 + 4i3 + 4i3 + 1i3x + -1i3x + 1i4 + -16x2 + 4x3 + -4x3 + x4) = 0
x(-8ix2 + 16i2 + -1i2x2 + -1i2x2 + 4i3 + 4i3 + 1i3x + -1i3x + 1i4 + -16x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: -1i2x2 + -1i2x2 = -2i2x2
x(-8ix2 + 16i2 + -2i2x2 + 4i3 + 4i3 + 1i3x + -1i3x + 1i4 + -16x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: 4i3 + 4i3 = 8i3
x(-8ix2 + 16i2 + -2i2x2 + 8i3 + 1i3x + -1i3x + 1i4 + -16x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: 1i3x + -1i3x = 0
x(-8ix2 + 16i2 + -2i2x2 + 8i3 + 0 + 1i4 + -16x2 + 4x3 + -4x3 + x4) = 0
x(-8ix2 + 16i2 + -2i2x2 + 8i3 + 1i4 + -16x2 + 4x3 + -4x3 + x4) = 0

Combine like terms: 4x3 + -4x3 = 0
x(-8ix2 + 16i2 + -2i2x2 + 8i3 + 1i4 + -16x2 + 0 + x4) = 0
x(-8ix2 + 16i2 + -2i2x2 + 8i3 + 1i4 + -16x2 + x4) = 0
(-8ix2 * x + 16i2 * x + -2i2x2 * x + 8i3 * x + 1i4 * x + -16x2 * x + x4 * x) = 0
(-8ix3 + 16i2x + -2i2x3 + 8i3x + 1i4x + -16x3 + x5) = 0

Solving
-8ix3 + 16i2x + -2i2x3 + 8i3x + 1i4x + -16x3 + x5 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8ix2 + 16i2 + -2i2x2 + 8i3 + i4 + -16x2 + x4) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-8ix2 + 16i2 + -2i2x2 + 8i3 + i4 + -16x2 + x4)' equal to zero and attempt to solve:

Simplifying
-8ix2 + 16i2 + -2i2x2 + 8i3 + i4 + -16x2 + x4 = 0

Solving
-8ix2 + 16i2 + -2i2x2 + 8i3 + i4 + -16x2 + x4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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