0=3x^3+(-1-3i)x^2+(-3-2i)x+(1+i)

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Solution for 0=3x^3+(-1-3i)x^2+(-3-2i)x+(1+i) equation: 


Simplifying
0 = 3x3 + (-1 + -3i) * x2 + (-3 + -2i) * x + (1 + i)

Reorder the terms for easier multiplication:
0 = 3x3 + x2(-1 + -3i) + (-3 + -2i) * x + (1 + i)
0 = 3x3 + (-1 * x2 + -3i * x2) + (-3 + -2i) * x + (1 + i)

Reorder the terms:
0 = 3x3 + (-3ix2 + -1x2) + (-3 + -2i) * x + (1 + i)
0 = 3x3 + (-3ix2 + -1x2) + (-3 + -2i) * x + (1 + i)

Reorder the terms for easier multiplication:
0 = 3x3 + -3ix2 + -1x2 + x(-3 + -2i) + (1 + i)
0 = 3x3 + -3ix2 + -1x2 + (-3 * x + -2i * x) + (1 + i)

Reorder the terms:
0 = 3x3 + -3ix2 + -1x2 + (-2ix + -3x) + (1 + i)
0 = 3x3 + -3ix2 + -1x2 + (-2ix + -3x) + (1 + i)

Remove parenthesis around (1 + i)
0 = 3x3 + -3ix2 + -1x2 + -2ix + -3x + 1 + i

Reorder the terms:
0 = 1 + i + -2ix + -3ix2 + -3x + -1x2 + 3x3

Solving
0 = 1 + i + -2ix + -3ix2 + -3x + -1x2 + 3x3

Solving for variable 'i'.

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

Add '-1i' to each side of the equation.
0 + -1i = 1 + i + -2ix + -3ix2 + -3x + -1x2 + -1i + 3x3
Remove the zero:
-1i = 1 + i + -2ix + -3ix2 + -3x + -1x2 + -1i + 3x3

Reorder the terms:
-1i = 1 + i + -1i + -2ix + -3ix2 + -3x + -1x2 + 3x3

Combine like terms: i + -1i = 0
-1i = 1 + 0 + -2ix + -3ix2 + -3x + -1x2 + 3x3
-1i = 1 + -2ix + -3ix2 + -3x + -1x2 + 3x3

Add '2ix' to each side of the equation.
-1i + 2ix = 1 + -2ix + -3ix2 + -3x + -1x2 + 2ix + 3x3

Reorder the terms:
-1i + 2ix = 1 + -2ix + 2ix + -3ix2 + -3x + -1x2 + 3x3

Combine like terms: -2ix + 2ix = 0
-1i + 2ix = 1 + 0 + -3ix2 + -3x + -1x2 + 3x3
-1i + 2ix = 1 + -3ix2 + -3x + -1x2 + 3x3

Add '3ix2' to each side of the equation.
-1i + 2ix + 3ix2 = 1 + -3ix2 + -3x + -1x2 + 3ix2 + 3x3

Reorder the terms:
-1i + 2ix + 3ix2 = 1 + -3ix2 + 3ix2 + -3x + -1x2 + 3x3

Combine like terms: -3ix2 + 3ix2 = 0
-1i + 2ix + 3ix2 = 1 + 0 + -3x + -1x2 + 3x3
-1i + 2ix + 3ix2 = 1 + -3x + -1x2 + 3x3

Reorder the terms:
-1 + -1i + 2ix + 3ix2 + 3x + x2 + -3x3 = 1 + -3x + -1x2 + 3x3 + -1 + 3x + x2 + -3x3

Reorder the terms:
-1 + -1i + 2ix + 3ix2 + 3x + x2 + -3x3 = 1 + -1 + -3x + 3x + -1x2 + x2 + 3x3 + -3x3

Combine like terms: 1 + -1 = 0
-1 + -1i + 2ix + 3ix2 + 3x + x2 + -3x3 = 0 + -3x + 3x + -1x2 + x2 + 3x3 + -3x3
-1 + -1i + 2ix + 3ix2 + 3x + x2 + -3x3 = -3x + 3x + -1x2 + x2 + 3x3 + -3x3

Combine like terms: -3x + 3x = 0
-1 + -1i + 2ix + 3ix2 + 3x + x2 + -3x3 = 0 + -1x2 + x2 + 3x3 + -3x3
-1 + -1i + 2ix + 3ix2 + 3x + x2 + -3x3 = -1x2 + x2 + 3x3 + -3x3

Combine like terms: -1x2 + x2 = 0
-1 + -1i + 2ix + 3ix2 + 3x + x2 + -3x3 = 0 + 3x3 + -3x3
-1 + -1i + 2ix + 3ix2 + 3x + x2 + -3x3 = 3x3 + -3x3

Combine like terms: 3x3 + -3x3 = 0
-1 + -1i + 2ix + 3ix2 + 3x + x2 + -3x3 = 0

The solution to this equation could not be determined.

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