(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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