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

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


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

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

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

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

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

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

Combine like terms: -3ix + -3ix = -6ix
(-6ix + 9i2 + x2) = 0

Solving
-6ix + 9i2 + x2 = 0

Solving for variable 'i'.

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


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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