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

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}