(x+2i)(x-2i)(x^2-4x-5)=0

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Solution for (x+2i)(x-2i)(x^2-4x-5)=0 equation: 


Simplifying
(x + 2i)(x + -2i)(x2 + -4x + -5) = 0

Reorder the terms:
(2i + x)(x + -2i)(x2 + -4x + -5) = 0

Reorder the terms:
(2i + x)(-2i + x)(x2 + -4x + -5) = 0

Reorder the terms:
(2i + x)(-2i + x)(-5 + -4x + x2) = 0

Multiply (2i + x) * (-2i + x)
(2i * (-2i + x) + x(-2i + x))(-5 + -4x + x2) = 0
((-2i * 2i + x * 2i) + x(-2i + x))(-5 + -4x + x2) = 0

Reorder the terms:
((2ix + -4i2) + x(-2i + x))(-5 + -4x + x2) = 0
((2ix + -4i2) + x(-2i + x))(-5 + -4x + x2) = 0
(2ix + -4i2 + (-2i * x + x * x))(-5 + -4x + x2) = 0
(2ix + -4i2 + (-2ix + x2))(-5 + -4x + x2) = 0

Reorder the terms:
(2ix + -2ix + -4i2 + x2)(-5 + -4x + x2) = 0

Combine like terms: 2ix + -2ix = 0
(0 + -4i2 + x2)(-5 + -4x + x2) = 0
(-4i2 + x2)(-5 + -4x + x2) = 0

Multiply (-4i2 + x2) * (-5 + -4x + x2)
(-4i2 * (-5 + -4x + x2) + x2(-5 + -4x + x2)) = 0
((-5 * -4i2 + -4x * -4i2 + x2 * -4i2) + x2(-5 + -4x + x2)) = 0
((20i2 + 16i2x + -4i2x2) + x2(-5 + -4x + x2)) = 0
(20i2 + 16i2x + -4i2x2 + (-5 * x2 + -4x * x2 + x2 * x2)) = 0
(20i2 + 16i2x + -4i2x2 + (-5x2 + -4x3 + x4)) = 0
(20i2 + 16i2x + -4i2x2 + -5x2 + -4x3 + x4) = 0

Solving
20i2 + 16i2x + -4i2x2 + -5x2 + -4x3 + x4 = 0

Solving for variable 'i'.

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

Add '5x2' to each side of the equation.
20i2 + 16i2x + -4i2x2 + -5x2 + -4x3 + 5x2 + x4 = 0 + 5x2

Reorder the terms:
20i2 + 16i2x + -4i2x2 + -5x2 + 5x2 + -4x3 + x4 = 0 + 5x2

Combine like terms: -5x2 + 5x2 = 0
20i2 + 16i2x + -4i2x2 + 0 + -4x3 + x4 = 0 + 5x2
20i2 + 16i2x + -4i2x2 + -4x3 + x4 = 0 + 5x2
Remove the zero:
20i2 + 16i2x + -4i2x2 + -4x3 + x4 = 5x2

Add '4x3' to each side of the equation.
20i2 + 16i2x + -4i2x2 + -4x3 + 4x3 + x4 = 5x2 + 4x3

Combine like terms: -4x3 + 4x3 = 0
20i2 + 16i2x + -4i2x2 + 0 + x4 = 5x2 + 4x3
20i2 + 16i2x + -4i2x2 + x4 = 5x2 + 4x3

Add '-1x4' to each side of the equation.
20i2 + 16i2x + -4i2x2 + x4 + -1x4 = 5x2 + 4x3 + -1x4

Combine like terms: x4 + -1x4 = 0
20i2 + 16i2x + -4i2x2 + 0 = 5x2 + 4x3 + -1x4
20i2 + 16i2x + -4i2x2 = 5x2 + 4x3 + -1x4

Reorder the terms:
20i2 + 16i2x + -4i2x2 + -5x2 + -4x3 + x4 = 5x2 + -5x2 + 4x3 + -4x3 + -1x4 + x4

Combine like terms: 5x2 + -5x2 = 0
20i2 + 16i2x + -4i2x2 + -5x2 + -4x3 + x4 = 0 + 4x3 + -4x3 + -1x4 + x4
20i2 + 16i2x + -4i2x2 + -5x2 + -4x3 + x4 = 4x3 + -4x3 + -1x4 + x4

Combine like terms: 4x3 + -4x3 = 0
20i2 + 16i2x + -4i2x2 + -5x2 + -4x3 + x4 = 0 + -1x4 + x4
20i2 + 16i2x + -4i2x2 + -5x2 + -4x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
20i2 + 16i2x + -4i2x2 + -5x2 + -4x3 + x4 = 0

The solution to this equation could not be determined.

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