(4-8i)(2i+1)=0

Solution for (4-8i)(2i+1)=0 equation:

Simplifying
(4 + -8i)(2i + 1) = 0

Reorder the terms:
(4 + -8i)(1 + 2i) = 0

Multiply (4 + -8i) * (1 + 2i)
(4(1 + 2i) + -8i * (1 + 2i)) = 0
((1 * 4 + 2i * 4) + -8i * (1 + 2i)) = 0
((4 + 8i) + -8i * (1 + 2i)) = 0
(4 + 8i + (1 * -8i + 2i * -8i)) = 0
(4 + 8i + (-8i + -16i2)) = 0

Combine like terms: 8i + -8i = 0
(4 + 0 + -16i2) = 0
(4 + -16i2) = 0

Solving
4 + -16i2 = 0

Solving for variable 'i'.

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

Add '-4' to each side of the equation.
4 + -4 + -16i2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -16i2 = 0 + -4
-16i2 = 0 + -4

Combine like terms: 0 + -4 = -4
-16i2 = -4

Divide each side by '-16'.
i2 = 0.25

Simplifying
i2 = 0.25

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