(2x-4i)(x+2i)=0

Solution for (2x-4i)(x+2i)=0 equation:

Simplifying
(2x + -4i)(x + 2i) = 0

Reorder the terms:
(-4i + 2x)(x + 2i) = 0

Reorder the terms:
(-4i + 2x)(2i + x) = 0

Multiply (-4i + 2x) * (2i + x)
(-4i * (2i + x) + 2x * (2i + x)) = 0
((2i * -4i + x * -4i) + 2x * (2i + x)) = 0

Reorder the terms:
((-4ix + -8i2) + 2x * (2i + x)) = 0
((-4ix + -8i2) + 2x * (2i + x)) = 0
(-4ix + -8i2 + (2i * 2x + x * 2x)) = 0
(-4ix + -8i2 + (4ix + 2x2)) = 0

Reorder the terms:
(-4ix + 4ix + -8i2 + 2x2) = 0

Combine like terms: -4ix + 4ix = 0
(0 + -8i2 + 2x2) = 0
(-8i2 + 2x2) = 0

Solving
-8i2 + 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.
-8i2 + 2x2 + -2x2 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8i2 + 0 = 0 + -2x2
-8i2 = 0 + -2x2
Remove the zero:
-8i2 = -2x2

Divide each side by '-8'.
i2 = 0.25x2

Simplifying
i2 = 0.25x2

Take the square root of each side:
i = {-0.5x, 0.5x}