x^3+3x^2+(3-6i)x+2i=0

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Solution for x^3+3x^2+(3-6i)x+2i=0 equation: 


Simplifying
x3 + 3x2 + (3 + -6i) * x + 2i = 0

Reorder the terms for easier multiplication:
x3 + 3x2 + x(3 + -6i) + 2i = 0
x3 + 3x2 + (3 * x + -6i * x) + 2i = 0

Reorder the terms:
x3 + 3x2 + (-6ix + 3x) + 2i = 0
x3 + 3x2 + (-6ix + 3x) + 2i = 0

Reorder the terms:
2i + -6ix + 3x + 3x2 + x3 = 0

Solving
2i + -6ix + 3x + 3x2 + x3 = 0

Solving for variable 'i'.

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

Add '-3x' to each side of the equation.
2i + -6ix + 3x + 3x2 + -3x + x3 = 0 + -3x

Reorder the terms:
2i + -6ix + 3x + -3x + 3x2 + x3 = 0 + -3x

Combine like terms: 3x + -3x = 0
2i + -6ix + 0 + 3x2 + x3 = 0 + -3x
2i + -6ix + 3x2 + x3 = 0 + -3x
Remove the zero:
2i + -6ix + 3x2 + x3 = -3x

Add '-3x2' to each side of the equation.
2i + -6ix + 3x2 + -3x2 + x3 = -3x + -3x2

Combine like terms: 3x2 + -3x2 = 0
2i + -6ix + 0 + x3 = -3x + -3x2
2i + -6ix + x3 = -3x + -3x2

Add '-1x3' to each side of the equation.
2i + -6ix + x3 + -1x3 = -3x + -3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
2i + -6ix + 0 = -3x + -3x2 + -1x3
2i + -6ix = -3x + -3x2 + -1x3

Reorder the terms:
2i + -6ix + 3x + 3x2 + x3 = -3x + 3x + -3x2 + 3x2 + -1x3 + x3

Combine like terms: -3x + 3x = 0
2i + -6ix + 3x + 3x2 + x3 = 0 + -3x2 + 3x2 + -1x3 + x3
2i + -6ix + 3x + 3x2 + x3 = -3x2 + 3x2 + -1x3 + x3

Combine like terms: -3x2 + 3x2 = 0
2i + -6ix + 3x + 3x2 + x3 = 0 + -1x3 + x3
2i + -6ix + 3x + 3x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
2i + -6ix + 3x + 3x2 + x3 = 0

The solution to this equation could not be determined.

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