x*3-(4+i)x*2+(1+2i)x+(6+3i)=0

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Solution for x*3-(4+i)x*2+(1+2i)x+(6+3i)=0 equation: 


Simplifying
x * 3 + -1(4 + i) * x * 2 + (1 + 2i) * x + (6 + 3i) = 0

Reorder the terms for easier multiplication:
3x + -1(4 + i) * x * 2 + (1 + 2i) * x + (6 + 3i) = 0

Reorder the terms for easier multiplication:
3x + -1 * 2x(4 + i) + (1 + 2i) * x + (6 + 3i) = 0

Multiply -1 * 2
3x + -2x(4 + i) + (1 + 2i) * x + (6 + 3i) = 0
3x + (4 * -2x + i * -2x) + (1 + 2i) * x + (6 + 3i) = 0

Reorder the terms:
3x + (-2ix + -8x) + (1 + 2i) * x + (6 + 3i) = 0
3x + (-2ix + -8x) + (1 + 2i) * x + (6 + 3i) = 0

Reorder the terms for easier multiplication:
3x + -2ix + -8x + x(1 + 2i) + (6 + 3i) = 0
3x + -2ix + -8x + (1 * x + 2i * x) + (6 + 3i) = 0

Reorder the terms:
3x + -2ix + -8x + (2ix + 1x) + (6 + 3i) = 0
3x + -2ix + -8x + (2ix + 1x) + (6 + 3i) = 0

Remove parenthesis around (6 + 3i)
3x + -2ix + -8x + 2ix + 1x + 6 + 3i = 0

Reorder the terms:
6 + 3i + -2ix + 2ix + 3x + -8x + 1x = 0

Combine like terms: -2ix + 2ix = 0
6 + 3i + 0 + 3x + -8x + 1x = 0
6 + 3i + 3x + -8x + 1x = 0

Combine like terms: 3x + -8x = -5x
6 + 3i + -5x + 1x = 0

Combine like terms: -5x + 1x = -4x
6 + 3i + -4x = 0

Solving
6 + 3i + -4x = 0

Solving for variable 'i'.

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

Add '-6' to each side of the equation.
6 + 3i + -6 + -4x = 0 + -6

Reorder the terms:
6 + -6 + 3i + -4x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 3i + -4x = 0 + -6
3i + -4x = 0 + -6

Combine like terms: 0 + -6 = -6
3i + -4x = -6

Add '4x' to each side of the equation.
3i + -4x + 4x = -6 + 4x

Combine like terms: -4x + 4x = 0
3i + 0 = -6 + 4x
3i = -6 + 4x

Divide each side by '3'.
i = -2 + 1.333333333x

Simplifying
i = -2 + 1.333333333x

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