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

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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 = -8ix
(-8ix + 8i2 + 2x2) = 0

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

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4ix + 4i2 + x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {0.5x, 0.5x}

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