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

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

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

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

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

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

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

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

Combine like terms: -2ix + ix = -1ix
(-1ix + -2i2 + x2) = 0

Solving
-1ix + -2i2 + x2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-1i + -1x)(2i + -1x) = 0

Subproblem 1
Set the factor '(-1i + -1x)' equal to zero and attempt to solve:

Simplifying
-1i + -1x = 0

Solving
-1i + -1x = 0

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

Add 'x' to each side of the equation.
-1i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-1i + 0 = 0 + x
-1i = 0 + x
Remove the zero:
-1i = x

Divide each side by '-1'.
i = -1x

Simplifying
i = -1x
Subproblem 2
Set the factor '(2i + -1x)' equal to zero and attempt to solve:

Simplifying
2i + -1x = 0

Solving
2i + -1x = 0

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

Add 'x' to each side of the equation.
2i + -1x + x = 0 + x

Combine like terms: -1x + x = 0
2i + 0 = 0 + x
2i = 0 + x
Remove the zero:
2i = x

Divide each side by '2'.
i = 0.5x

Simplifying
i = 0.5x
Solution
i = {-1x, 0.5x}