(2x-6i)(x+3i)=

Solution for (2x-6i)(x+3i)= equation:

Simplifying
(2x + -6i)(x + 3i) = 0

Reorder the terms:
(-6i + 2x)(x + 3i) = 0

Reorder the terms:
(-6i + 2x)(3i + x) = 0

Multiply (-6i + 2x) * (3i + x)
(-6i * (3i + x) + 2x * (3i + x)) = 0
((3i * -6i + x * -6i) + 2x * (3i + x)) = 0

Reorder the terms:
((-6ix + -18i2) + 2x * (3i + x)) = 0
((-6ix + -18i2) + 2x * (3i + x)) = 0
(-6ix + -18i2 + (3i * 2x + x * 2x)) = 0
(-6ix + -18i2 + (6ix + 2x2)) = 0

Reorder the terms:
(-6ix + 6ix + -18i2 + 2x2) = 0

Combine like terms: -6ix + 6ix = 0
(0 + -18i2 + 2x2) = 0
(-18i2 + 2x2) = 0

Solving
-18i2 + 2x2 = 0

Solving for variable 'i'.

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

Add '-2x2' to each side of the equation.
-18i2 + 2x2 + -2x2 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18i2 + 0 = 0 + -2x2
-18i2 = 0 + -2x2
Remove the zero:
-18i2 = -2x2

Divide each side by '-18'.
i2 = 0.1111111111x2

Simplifying
i2 = 0.1111111111x2

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