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

Ignore the factor 2.

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

Simplifying
2i + x = 0

Solving
2i + x = 0

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

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

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

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

Simplifying
i = -0.5x

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

Simplifying
2i + x = 0

Solving
2i + x = 0

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

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

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

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

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

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