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

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


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

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

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

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

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

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

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

Reorder the terms:
((18ix + 54i2) + -3ix * (3i + x) + -6x * (3i + x) + x2(3i + x)) = 0
((18ix + 54i2) + -3ix * (3i + x) + -6x * (3i + x) + x2(3i + x)) = 0
(18ix + 54i2 + (3i * -3ix + x * -3ix) + -6x * (3i + x) + x2(3i + x)) = 0

Reorder the terms:
(18ix + 54i2 + (-3ix2 + -9i2x) + -6x * (3i + x) + x2(3i + x)) = 0
(18ix + 54i2 + (-3ix2 + -9i2x) + -6x * (3i + x) + x2(3i + x)) = 0
(18ix + 54i2 + -3ix2 + -9i2x + (3i * -6x + x * -6x) + x2(3i + x)) = 0
(18ix + 54i2 + -3ix2 + -9i2x + (-18ix + -6x2) + x2(3i + x)) = 0
(18ix + 54i2 + -3ix2 + -9i2x + -18ix + -6x2 + (3i * x2 + x * x2)) = 0
(18ix + 54i2 + -3ix2 + -9i2x + -18ix + -6x2 + (3ix2 + x3)) = 0

Reorder the terms:
(18ix + -18ix + -3ix2 + 3ix2 + 54i2 + -9i2x + -6x2 + x3) = 0

Combine like terms: 18ix + -18ix = 0
(0 + -3ix2 + 3ix2 + 54i2 + -9i2x + -6x2 + x3) = 0
(-3ix2 + 3ix2 + 54i2 + -9i2x + -6x2 + x3) = 0

Combine like terms: -3ix2 + 3ix2 = 0
(0 + 54i2 + -9i2x + -6x2 + x3) = 0
(54i2 + -9i2x + -6x2 + x3) = 0

Solving
54i2 + -9i2x + -6x2 + x3 = 0

Solving for variable 'i'.

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

Add '6x2' to each side of the equation.
54i2 + -9i2x + -6x2 + 6x2 + x3 = 0 + 6x2

Combine like terms: -6x2 + 6x2 = 0
54i2 + -9i2x + 0 + x3 = 0 + 6x2
54i2 + -9i2x + x3 = 0 + 6x2
Remove the zero:
54i2 + -9i2x + x3 = 6x2

Add '-1x3' to each side of the equation.
54i2 + -9i2x + x3 + -1x3 = 6x2 + -1x3

Combine like terms: x3 + -1x3 = 0
54i2 + -9i2x + 0 = 6x2 + -1x3
54i2 + -9i2x = 6x2 + -1x3

Reorder the terms:
54i2 + -9i2x + -6x2 + x3 = 6x2 + -6x2 + -1x3 + x3

Combine like terms: 6x2 + -6x2 = 0
54i2 + -9i2x + -6x2 + x3 = 0 + -1x3 + x3
54i2 + -9i2x + -6x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
54i2 + -9i2x + -6x2 + x3 = 0

The solution to this equation could not be determined.

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