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

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


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

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

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

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

Multiply (4 + x) * (4i + x)
(4(4i + x) + x(4i + x))(-4i + x) = 0
((4i * 4 + x * 4) + x(4i + x))(-4i + x) = 0
((16i + 4x) + x(4i + x))(-4i + x) = 0
(16i + 4x + (4i * x + x * x))(-4i + x) = 0
(16i + 4x + (4ix + x2))(-4i + x) = 0

Reorder the terms:
(16i + 4ix + 4x + x2)(-4i + x) = 0
(16i + 4ix + 4x + x2)(-4i + x) = 0

Multiply (16i + 4ix + 4x + x2) * (-4i + x)
(16i * (-4i + x) + 4ix * (-4i + x) + 4x * (-4i + x) + x2(-4i + x)) = 0
((-4i * 16i + x * 16i) + 4ix * (-4i + x) + 4x * (-4i + x) + x2(-4i + x)) = 0

Reorder the terms:
((16ix + -64i2) + 4ix * (-4i + x) + 4x * (-4i + x) + x2(-4i + x)) = 0
((16ix + -64i2) + 4ix * (-4i + x) + 4x * (-4i + x) + x2(-4i + x)) = 0
(16ix + -64i2 + (-4i * 4ix + x * 4ix) + 4x * (-4i + x) + x2(-4i + x)) = 0

Reorder the terms:
(16ix + -64i2 + (4ix2 + -16i2x) + 4x * (-4i + x) + x2(-4i + x)) = 0
(16ix + -64i2 + (4ix2 + -16i2x) + 4x * (-4i + x) + x2(-4i + x)) = 0
(16ix + -64i2 + 4ix2 + -16i2x + (-4i * 4x + x * 4x) + x2(-4i + x)) = 0
(16ix + -64i2 + 4ix2 + -16i2x + (-16ix + 4x2) + x2(-4i + x)) = 0
(16ix + -64i2 + 4ix2 + -16i2x + -16ix + 4x2 + (-4i * x2 + x * x2)) = 0
(16ix + -64i2 + 4ix2 + -16i2x + -16ix + 4x2 + (-4ix2 + x3)) = 0

Reorder the terms:
(16ix + -16ix + 4ix2 + -4ix2 + -64i2 + -16i2x + 4x2 + x3) = 0

Combine like terms: 16ix + -16ix = 0
(0 + 4ix2 + -4ix2 + -64i2 + -16i2x + 4x2 + x3) = 0
(4ix2 + -4ix2 + -64i2 + -16i2x + 4x2 + x3) = 0

Combine like terms: 4ix2 + -4ix2 = 0
(0 + -64i2 + -16i2x + 4x2 + x3) = 0
(-64i2 + -16i2x + 4x2 + x3) = 0

Solving
-64i2 + -16i2x + 4x2 + x3 = 0

Solving for variable 'i'.

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

Add '-4x2' to each side of the equation.
-64i2 + -16i2x + 4x2 + -4x2 + x3 = 0 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-64i2 + -16i2x + 0 + x3 = 0 + -4x2
-64i2 + -16i2x + x3 = 0 + -4x2
Remove the zero:
-64i2 + -16i2x + x3 = -4x2

Add '-1x3' to each side of the equation.
-64i2 + -16i2x + x3 + -1x3 = -4x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-64i2 + -16i2x + 0 = -4x2 + -1x3
-64i2 + -16i2x = -4x2 + -1x3

Reorder the terms:
-64i2 + -16i2x + 4x2 + x3 = -4x2 + 4x2 + -1x3 + x3

Combine like terms: -4x2 + 4x2 = 0
-64i2 + -16i2x + 4x2 + x3 = 0 + -1x3 + x3
-64i2 + -16i2x + 4x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-64i2 + -16i2x + 4x2 + x3 = 0

The solution to this equation could not be determined.

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