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

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


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

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

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

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

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

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

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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