(3x-9i)(x-3i)=0

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Solution for (3x-9i)(x-3i)=0 equation: 


Simplifying
(3x + -9i)(x + -3i) = 0

Reorder the terms:
(-9i + 3x)(x + -3i) = 0

Reorder the terms:
(-9i + 3x)(-3i + x) = 0

Multiply (-9i + 3x) * (-3i + x)
(-9i * (-3i + x) + 3x * (-3i + x)) = 0
((-3i * -9i + x * -9i) + 3x * (-3i + x)) = 0

Reorder the terms:
((-9ix + 27i2) + 3x * (-3i + x)) = 0
((-9ix + 27i2) + 3x * (-3i + x)) = 0
(-9ix + 27i2 + (-3i * 3x + x * 3x)) = 0
(-9ix + 27i2 + (-9ix + 3x2)) = 0

Reorder the terms:
(-9ix + -9ix + 27i2 + 3x2) = 0

Combine like terms: -9ix + -9ix = -18ix
(-18ix + 27i2 + 3x2) = 0

Solving
-18ix + 27i2 + 3x2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6ix + 9i2 + x2) = 0

Factor a trinomial.
3((3i + -1x)(3i + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3i + -1x)' equal to zero and attempt to solve:

Simplifying
3i + -1x = 0

Solving
3i + -1x = 0

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

Add 'x' to each side of the equation.
3i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
3i + 0 = 0 + x
3i = 0 + x
Remove the zero:
3i = x

Divide each side by '3'.
i = 0.3333333333x

Simplifying
i = 0.3333333333x

Subproblem 2
Set the factor '(3i + -1x)' equal to zero and attempt to solve:

Simplifying
3i + -1x = 0

Solving
3i + -1x = 0

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

Add 'x' to each side of the equation.
3i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
3i + 0 = 0 + x
3i = 0 + x
Remove the zero:
3i = x

Divide each side by '3'.
i = 0.3333333333x

Simplifying
i = 0.3333333333x
Solution
i = {0.3333333333x, 0.3333333333x}

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