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

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


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

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

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

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

Multiply (-5 + x) * (-4i + x)
(-5(-4i + x) + x(-4i + x))(4i + x) = 0
((-4i * -5 + x * -5) + x(-4i + x))(4i + x) = 0
((20i + -5x) + x(-4i + x))(4i + x) = 0
(20i + -5x + (-4i * x + x * x))(4i + x) = 0
(20i + -5x + (-4ix + x2))(4i + x) = 0

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

Multiply (20i + -4ix + -5x + x2) * (4i + x)
(20i * (4i + x) + -4ix * (4i + x) + -5x * (4i + x) + x2(4i + x)) = 0
((4i * 20i + x * 20i) + -4ix * (4i + x) + -5x * (4i + x) + x2(4i + x)) = 0

Reorder the terms:
((20ix + 80i2) + -4ix * (4i + x) + -5x * (4i + x) + x2(4i + x)) = 0
((20ix + 80i2) + -4ix * (4i + x) + -5x * (4i + x) + x2(4i + x)) = 0
(20ix + 80i2 + (4i * -4ix + x * -4ix) + -5x * (4i + x) + x2(4i + x)) = 0

Reorder the terms:
(20ix + 80i2 + (-4ix2 + -16i2x) + -5x * (4i + x) + x2(4i + x)) = 0
(20ix + 80i2 + (-4ix2 + -16i2x) + -5x * (4i + x) + x2(4i + x)) = 0
(20ix + 80i2 + -4ix2 + -16i2x + (4i * -5x + x * -5x) + x2(4i + x)) = 0
(20ix + 80i2 + -4ix2 + -16i2x + (-20ix + -5x2) + x2(4i + x)) = 0
(20ix + 80i2 + -4ix2 + -16i2x + -20ix + -5x2 + (4i * x2 + x * x2)) = 0
(20ix + 80i2 + -4ix2 + -16i2x + -20ix + -5x2 + (4ix2 + x3)) = 0

Reorder the terms:
(20ix + -20ix + -4ix2 + 4ix2 + 80i2 + -16i2x + -5x2 + x3) = 0

Combine like terms: 20ix + -20ix = 0
(0 + -4ix2 + 4ix2 + 80i2 + -16i2x + -5x2 + x3) = 0
(-4ix2 + 4ix2 + 80i2 + -16i2x + -5x2 + x3) = 0

Combine like terms: -4ix2 + 4ix2 = 0
(0 + 80i2 + -16i2x + -5x2 + x3) = 0
(80i2 + -16i2x + -5x2 + x3) = 0

Solving
80i2 + -16i2x + -5x2 + x3 = 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.
80i2 + -16i2x + -5x2 + 5x2 + x3 = 0 + 5x2

Combine like terms: -5x2 + 5x2 = 0
80i2 + -16i2x + 0 + x3 = 0 + 5x2
80i2 + -16i2x + x3 = 0 + 5x2
Remove the zero:
80i2 + -16i2x + x3 = 5x2

Add '-1x3' to each side of the equation.
80i2 + -16i2x + x3 + -1x3 = 5x2 + -1x3

Combine like terms: x3 + -1x3 = 0
80i2 + -16i2x + 0 = 5x2 + -1x3
80i2 + -16i2x = 5x2 + -1x3

Reorder the terms:
80i2 + -16i2x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3

Combine like terms: 5x2 + -5x2 = 0
80i2 + -16i2x + -5x2 + x3 = 0 + -1x3 + x3
80i2 + -16i2x + -5x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
80i2 + -16i2x + -5x2 + x3 = 0

The solution to this equation could not be determined.

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