(-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 = 0
(0 + 27i2 + -3x2) = 0
(27i2 + -3x2) = 0

Solving
27i2 + -3x2 = 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.
27i2 + -3x2 + 3x2 = 0 + 3x2

Combine like terms: -3x2 + 3x2 = 0
27i2 + 0 = 0 + 3x2
27i2 = 0 + 3x2
Remove the zero:
27i2 = 3x2

Divide each side by '27'.
i2 = 0.1111111111x2

Simplifying
i2 = 0.1111111111x2

Take the square root of each side:
i = {-0.333333333x, 0.333333333x}

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