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

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


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

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

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

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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