(x+3)(x+6i)(x-6i)=0

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Solution for (x+3)(x+6i)(x-6i)=0 equation: 


Simplifying
(x + 3)(x + 6i)(x + -6i) = 0

Reorder the terms:
(3 + x)(x + 6i)(x + -6i) = 0

Reorder the terms:
(3 + x)(6i + x)(x + -6i) = 0

Reorder the terms:
(3 + x)(6i + x)(-6i + x) = 0

Multiply (3 + x) * (6i + x)
(3(6i + x) + x(6i + x))(-6i + x) = 0
((6i * 3 + x * 3) + x(6i + x))(-6i + x) = 0
((18i + 3x) + x(6i + x))(-6i + x) = 0
(18i + 3x + (6i * x + x * x))(-6i + x) = 0
(18i + 3x + (6ix + x2))(-6i + x) = 0

Reorder the terms:
(18i + 6ix + 3x + x2)(-6i + x) = 0
(18i + 6ix + 3x + x2)(-6i + x) = 0

Multiply (18i + 6ix + 3x + x2) * (-6i + x)
(18i * (-6i + x) + 6ix * (-6i + x) + 3x * (-6i + x) + x2(-6i + x)) = 0
((-6i * 18i + x * 18i) + 6ix * (-6i + x) + 3x * (-6i + x) + x2(-6i + x)) = 0

Reorder the terms:
((18ix + -108i2) + 6ix * (-6i + x) + 3x * (-6i + x) + x2(-6i + x)) = 0
((18ix + -108i2) + 6ix * (-6i + x) + 3x * (-6i + x) + x2(-6i + x)) = 0
(18ix + -108i2 + (-6i * 6ix + x * 6ix) + 3x * (-6i + x) + x2(-6i + x)) = 0

Reorder the terms:
(18ix + -108i2 + (6ix2 + -36i2x) + 3x * (-6i + x) + x2(-6i + x)) = 0
(18ix + -108i2 + (6ix2 + -36i2x) + 3x * (-6i + x) + x2(-6i + x)) = 0
(18ix + -108i2 + 6ix2 + -36i2x + (-6i * 3x + x * 3x) + x2(-6i + x)) = 0
(18ix + -108i2 + 6ix2 + -36i2x + (-18ix + 3x2) + x2(-6i + x)) = 0
(18ix + -108i2 + 6ix2 + -36i2x + -18ix + 3x2 + (-6i * x2 + x * x2)) = 0
(18ix + -108i2 + 6ix2 + -36i2x + -18ix + 3x2 + (-6ix2 + x3)) = 0

Reorder the terms:
(18ix + -18ix + 6ix2 + -6ix2 + -108i2 + -36i2x + 3x2 + x3) = 0

Combine like terms: 18ix + -18ix = 0
(0 + 6ix2 + -6ix2 + -108i2 + -36i2x + 3x2 + x3) = 0
(6ix2 + -6ix2 + -108i2 + -36i2x + 3x2 + x3) = 0

Combine like terms: 6ix2 + -6ix2 = 0
(0 + -108i2 + -36i2x + 3x2 + x3) = 0
(-108i2 + -36i2x + 3x2 + x3) = 0

Solving
-108i2 + -36i2x + 3x2 + x3 = 0

Solving for variable 'i'.

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

Add '-3x2' to each side of the equation.
-108i2 + -36i2x + 3x2 + -3x2 + x3 = 0 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-108i2 + -36i2x + 0 + x3 = 0 + -3x2
-108i2 + -36i2x + x3 = 0 + -3x2
Remove the zero:
-108i2 + -36i2x + x3 = -3x2

Add '-1x3' to each side of the equation.
-108i2 + -36i2x + x3 + -1x3 = -3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-108i2 + -36i2x + 0 = -3x2 + -1x3
-108i2 + -36i2x = -3x2 + -1x3

Reorder the terms:
-108i2 + -36i2x + 3x2 + x3 = -3x2 + 3x2 + -1x3 + x3

Combine like terms: -3x2 + 3x2 = 0
-108i2 + -36i2x + 3x2 + x3 = 0 + -1x3 + x3
-108i2 + -36i2x + 3x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-108i2 + -36i2x + 3x2 + x3 = 0

The solution to this equation could not be determined.

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