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

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


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

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

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

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

Multiply (-5 + x) * (-4 + -2i + x)
(-5(-4 + -2i + x) + x(-4 + -2i + x))(4 + 2i + x) = 0
((-4 * -5 + -2i * -5 + x * -5) + x(-4 + -2i + x))(4 + 2i + x) = 0
((20 + 10i + -5x) + x(-4 + -2i + x))(4 + 2i + x) = 0
(20 + 10i + -5x + (-4 * x + -2i * x + x * x))(4 + 2i + x) = 0

Reorder the terms:
(20 + 10i + -5x + (-2ix + -4x + x2))(4 + 2i + x) = 0
(20 + 10i + -5x + (-2ix + -4x + x2))(4 + 2i + x) = 0

Reorder the terms:
(20 + 10i + -2ix + -5x + -4x + x2)(4 + 2i + x) = 0

Combine like terms: -5x + -4x = -9x
(20 + 10i + -2ix + -9x + x2)(4 + 2i + x) = 0

Multiply (20 + 10i + -2ix + -9x + x2) * (4 + 2i + x)
(20(4 + 2i + x) + 10i * (4 + 2i + x) + -2ix * (4 + 2i + x) + -9x * (4 + 2i + x) + x2(4 + 2i + x)) = 0
((4 * 20 + 2i * 20 + x * 20) + 10i * (4 + 2i + x) + -2ix * (4 + 2i + x) + -9x * (4 + 2i + x) + x2(4 + 2i + x)) = 0
((80 + 40i + 20x) + 10i * (4 + 2i + x) + -2ix * (4 + 2i + x) + -9x * (4 + 2i + x) + x2(4 + 2i + x)) = 0
(80 + 40i + 20x + (4 * 10i + 2i * 10i + x * 10i) + -2ix * (4 + 2i + x) + -9x * (4 + 2i + x) + x2(4 + 2i + x)) = 0

Reorder the terms:
(80 + 40i + 20x + (40i + 10ix + 20i2) + -2ix * (4 + 2i + x) + -9x * (4 + 2i + x) + x2(4 + 2i + x)) = 0
(80 + 40i + 20x + (40i + 10ix + 20i2) + -2ix * (4 + 2i + x) + -9x * (4 + 2i + x) + x2(4 + 2i + x)) = 0
(80 + 40i + 20x + 40i + 10ix + 20i2 + (4 * -2ix + 2i * -2ix + x * -2ix) + -9x * (4 + 2i + x) + x2(4 + 2i + x)) = 0

Reorder the terms:
(80 + 40i + 20x + 40i + 10ix + 20i2 + (-8ix + -2ix2 + -4i2x) + -9x * (4 + 2i + x) + x2(4 + 2i + x)) = 0
(80 + 40i + 20x + 40i + 10ix + 20i2 + (-8ix + -2ix2 + -4i2x) + -9x * (4 + 2i + x) + x2(4 + 2i + x)) = 0
(80 + 40i + 20x + 40i + 10ix + 20i2 + -8ix + -2ix2 + -4i2x + (4 * -9x + 2i * -9x + x * -9x) + x2(4 + 2i + x)) = 0

Reorder the terms:
(80 + 40i + 20x + 40i + 10ix + 20i2 + -8ix + -2ix2 + -4i2x + (-18ix + -36x + -9x2) + x2(4 + 2i + x)) = 0
(80 + 40i + 20x + 40i + 10ix + 20i2 + -8ix + -2ix2 + -4i2x + (-18ix + -36x + -9x2) + x2(4 + 2i + x)) = 0
(80 + 40i + 20x + 40i + 10ix + 20i2 + -8ix + -2ix2 + -4i2x + -18ix + -36x + -9x2 + (4 * x2 + 2i * x2 + x * x2)) = 0

Reorder the terms:
(80 + 40i + 20x + 40i + 10ix + 20i2 + -8ix + -2ix2 + -4i2x + -18ix + -36x + -9x2 + (2ix2 + 4x2 + x3)) = 0
(80 + 40i + 20x + 40i + 10ix + 20i2 + -8ix + -2ix2 + -4i2x + -18ix + -36x + -9x2 + (2ix2 + 4x2 + x3)) = 0

Reorder the terms:
(80 + 40i + 40i + 10ix + -8ix + -18ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 20x + -36x + -9x2 + 4x2 + x3) = 0

Combine like terms: 40i + 40i = 80i
(80 + 80i + 10ix + -8ix + -18ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 20x + -36x + -9x2 + 4x2 + x3) = 0

Combine like terms: 10ix + -8ix = 2ix
(80 + 80i + 2ix + -18ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 20x + -36x + -9x2 + 4x2 + x3) = 0

Combine like terms: 2ix + -18ix = -16ix
(80 + 80i + -16ix + -2ix2 + 2ix2 + 20i2 + -4i2x + 20x + -36x + -9x2 + 4x2 + x3) = 0

Combine like terms: -2ix2 + 2ix2 = 0
(80 + 80i + -16ix + 0 + 20i2 + -4i2x + 20x + -36x + -9x2 + 4x2 + x3) = 0
(80 + 80i + -16ix + 20i2 + -4i2x + 20x + -36x + -9x2 + 4x2 + x3) = 0

Combine like terms: 20x + -36x = -16x
(80 + 80i + -16ix + 20i2 + -4i2x + -16x + -9x2 + 4x2 + x3) = 0

Combine like terms: -9x2 + 4x2 = -5x2
(80 + 80i + -16ix + 20i2 + -4i2x + -16x + -5x2 + x3) = 0

Solving
80 + 80i + -16ix + 20i2 + -4i2x + -16x + -5x2 + x3 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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