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

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


Simplifying
x6 + (3 + i) * x3 + 3i = 0

Reorder the terms for easier multiplication:
x6 + x3(3 + i) + 3i = 0
x6 + (3 * x3 + i * x3) + 3i = 0

Reorder the terms:
x6 + (ix3 + 3x3) + 3i = 0
x6 + (ix3 + 3x3) + 3i = 0

Reorder the terms:
3i + ix3 + 3x3 + x6 = 0

Solving
3i + ix3 + 3x3 + x6 = 0

Solving for variable 'i'.

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

Add '-3x3' to each side of the equation.
3i + ix3 + 3x3 + -3x3 + x6 = 0 + -3x3

Combine like terms: 3x3 + -3x3 = 0
3i + ix3 + 0 + x6 = 0 + -3x3
3i + ix3 + x6 = 0 + -3x3
Remove the zero:
3i + ix3 + x6 = -3x3

Add '-1x6' to each side of the equation.
3i + ix3 + x6 + -1x6 = -3x3 + -1x6

Combine like terms: x6 + -1x6 = 0
3i + ix3 + 0 = -3x3 + -1x6
3i + ix3 = -3x3 + -1x6

Reorder the terms:
3i + ix3 + 3x3 + x6 = -3x3 + 3x3 + -1x6 + x6

Combine like terms: -3x3 + 3x3 = 0
3i + ix3 + 3x3 + x6 = 0 + -1x6 + x6
3i + ix3 + 3x3 + x6 = -1x6 + x6

Combine like terms: -1x6 + x6 = 0
3i + ix3 + 3x3 + x6 = 0

The solution to this equation could not be determined.

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