(x+1)(x-3)(x-i)(x+i)=0

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Solution for (x+1)(x-3)(x-i)(x+i)=0 equation: 


Simplifying
(x + 1)(x + -3)(x + -1i)(x + i) = 0

Reorder the terms:
(1 + x)(x + -3)(x + -1i)(x + i) = 0

Reorder the terms:
(1 + x)(-3 + x)(x + -1i)(x + i) = 0

Reorder the terms:
(1 + x)(-3 + x)(-1i + x)(x + i) = 0

Reorder the terms:
(1 + x)(-3 + x)(-1i + x)(i + x) = 0

Multiply (1 + x) * (-3 + x)
(1(-3 + x) + x(-3 + x))(-1i + x)(i + x) = 0
((-3 * 1 + x * 1) + x(-3 + x))(-1i + x)(i + x) = 0
((-3 + 1x) + x(-3 + x))(-1i + x)(i + x) = 0
(-3 + 1x + (-3 * x + x * x))(-1i + x)(i + x) = 0
(-3 + 1x + (-3x + x2))(-1i + x)(i + x) = 0

Combine like terms: 1x + -3x = -2x
(-3 + -2x + x2)(-1i + x)(i + x) = 0

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

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

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

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

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

Reorder the terms:
(3ix + 3i2 + 2ix2 + 2i2x + (-1ix3 + -1i2x2) + -3x * (i + x) + -2x2 * (i + x) + x3(i + x)) = 0
(3ix + 3i2 + 2ix2 + 2i2x + (-1ix3 + -1i2x2) + -3x * (i + x) + -2x2 * (i + x) + x3(i + x)) = 0
(3ix + 3i2 + 2ix2 + 2i2x + -1ix3 + -1i2x2 + (i * -3x + x * -3x) + -2x2 * (i + x) + x3(i + x)) = 0
(3ix + 3i2 + 2ix2 + 2i2x + -1ix3 + -1i2x2 + (-3ix + -3x2) + -2x2 * (i + x) + x3(i + x)) = 0
(3ix + 3i2 + 2ix2 + 2i2x + -1ix3 + -1i2x2 + -3ix + -3x2 + (i * -2x2 + x * -2x2) + x3(i + x)) = 0
(3ix + 3i2 + 2ix2 + 2i2x + -1ix3 + -1i2x2 + -3ix + -3x2 + (-2ix2 + -2x3) + x3(i + x)) = 0
(3ix + 3i2 + 2ix2 + 2i2x + -1ix3 + -1i2x2 + -3ix + -3x2 + -2ix2 + -2x3 + (i * x3 + x * x3)) = 0
(3ix + 3i2 + 2ix2 + 2i2x + -1ix3 + -1i2x2 + -3ix + -3x2 + -2ix2 + -2x3 + (ix3 + x4)) = 0

Reorder the terms:
(3ix + -3ix + 2ix2 + -2ix2 + -1ix3 + ix3 + 3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4) = 0

Combine like terms: 3ix + -3ix = 0
(0 + 2ix2 + -2ix2 + -1ix3 + ix3 + 3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4) = 0
(2ix2 + -2ix2 + -1ix3 + ix3 + 3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4) = 0

Combine like terms: 2ix2 + -2ix2 = 0
(0 + -1ix3 + ix3 + 3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4) = 0
(-1ix3 + ix3 + 3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4) = 0

Combine like terms: -1ix3 + ix3 = 0
(0 + 3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4) = 0
(3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4) = 0

Solving
3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4 = 0

Solving for variable 'i'.

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

Add '3x2' to each side of the equation.
3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + 3x2 + x4 = 0 + 3x2

Reorder the terms:
3i2 + 2i2x + -1i2x2 + -3x2 + 3x2 + -2x3 + x4 = 0 + 3x2

Combine like terms: -3x2 + 3x2 = 0
3i2 + 2i2x + -1i2x2 + 0 + -2x3 + x4 = 0 + 3x2
3i2 + 2i2x + -1i2x2 + -2x3 + x4 = 0 + 3x2
Remove the zero:
3i2 + 2i2x + -1i2x2 + -2x3 + x4 = 3x2

Add '2x3' to each side of the equation.
3i2 + 2i2x + -1i2x2 + -2x3 + 2x3 + x4 = 3x2 + 2x3

Combine like terms: -2x3 + 2x3 = 0
3i2 + 2i2x + -1i2x2 + 0 + x4 = 3x2 + 2x3
3i2 + 2i2x + -1i2x2 + x4 = 3x2 + 2x3

Add '-1x4' to each side of the equation.
3i2 + 2i2x + -1i2x2 + x4 + -1x4 = 3x2 + 2x3 + -1x4

Combine like terms: x4 + -1x4 = 0
3i2 + 2i2x + -1i2x2 + 0 = 3x2 + 2x3 + -1x4
3i2 + 2i2x + -1i2x2 = 3x2 + 2x3 + -1x4

Reorder the terms:
3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4 = 3x2 + -3x2 + 2x3 + -2x3 + -1x4 + x4

Combine like terms: 3x2 + -3x2 = 0
3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4 = 0 + 2x3 + -2x3 + -1x4 + x4
3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4 = 2x3 + -2x3 + -1x4 + x4

Combine like terms: 2x3 + -2x3 = 0
3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4 = 0 + -1x4 + x4
3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
3i2 + 2i2x + -1i2x2 + -3x2 + -2x3 + x4 = 0

The solution to this equation could not be determined.

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