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

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 = 0
(0 + -9i2 + x2) = 0
(-9i2 + x2) = 0

Solving
-9i2 + x2 = 0

Solving for variable 'i'.

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

Add '-1x2' to each side of the equation.
-9i2 + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
-9i2 + 0 = 0 + -1x2
-9i2 = 0 + -1x2
Remove the zero:
-9i2 = -1x2

Divide each side by '-9'.
i2 = 0.1111111111x2

Simplifying
i2 = 0.1111111111x2

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