(3x-y)(2+i)+(x-iy)(1+2i)=5+6i

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Solution for (3x-y)(2+i)+(x-iy)(1+2i)=5+6i equation: 


Simplifying
(3x + -1y)(2 + i) + (x + -1iy)(1 + 2i) = 5 + 6i

Multiply (3x + -1y) * (2 + i)
(3x * (2 + i) + -1y * (2 + i)) + (x + -1iy)(1 + 2i) = 5 + 6i
((2 * 3x + i * 3x) + -1y * (2 + i)) + (x + -1iy)(1 + 2i) = 5 + 6i

Reorder the terms:
((3ix + 6x) + -1y * (2 + i)) + (x + -1iy)(1 + 2i) = 5 + 6i
((3ix + 6x) + -1y * (2 + i)) + (x + -1iy)(1 + 2i) = 5 + 6i
(3ix + 6x + (2 * -1y + i * -1y)) + (x + -1iy)(1 + 2i) = 5 + 6i

Reorder the terms:
(3ix + 6x + (-1iy + -2y)) + (x + -1iy)(1 + 2i) = 5 + 6i
(3ix + 6x + (-1iy + -2y)) + (x + -1iy)(1 + 2i) = 5 + 6i

Reorder the terms:
(3ix + -1iy + 6x + -2y) + (x + -1iy)(1 + 2i) = 5 + 6i
(3ix + -1iy + 6x + -2y) + (x + -1iy)(1 + 2i) = 5 + 6i

Reorder the terms:
3ix + -1iy + 6x + -2y + (-1iy + x)(1 + 2i) = 5 + 6i

Multiply (-1iy + x) * (1 + 2i)
3ix + -1iy + 6x + -2y + (-1iy * (1 + 2i) + x(1 + 2i)) = 5 + 6i
3ix + -1iy + 6x + -2y + ((1 * -1iy + 2i * -1iy) + x(1 + 2i)) = 5 + 6i
3ix + -1iy + 6x + -2y + ((-1iy + -2i2y) + x(1 + 2i)) = 5 + 6i
3ix + -1iy + 6x + -2y + (-1iy + -2i2y + (1 * x + 2i * x)) = 5 + 6i

Reorder the terms:
3ix + -1iy + 6x + -2y + (-1iy + -2i2y + (2ix + 1x)) = 5 + 6i
3ix + -1iy + 6x + -2y + (-1iy + -2i2y + (2ix + 1x)) = 5 + 6i

Reorder the terms:
3ix + -1iy + 6x + -2y + (2ix + -1iy + -2i2y + 1x) = 5 + 6i
3ix + -1iy + 6x + -2y + (2ix + -1iy + -2i2y + 1x) = 5 + 6i

Reorder the terms:
3ix + 2ix + -1iy + -1iy + -2i2y + 6x + 1x + -2y = 5 + 6i

Combine like terms: 3ix + 2ix = 5ix
5ix + -1iy + -1iy + -2i2y + 6x + 1x + -2y = 5 + 6i

Combine like terms: -1iy + -1iy = -2iy
5ix + -2iy + -2i2y + 6x + 1x + -2y = 5 + 6i

Combine like terms: 6x + 1x = 7x
5ix + -2iy + -2i2y + 7x + -2y = 5 + 6i

Solving
5ix + -2iy + -2i2y + 7x + -2y = 5 + 6i

Solving for variable 'i'.

Reorder the terms:
-5 + -6i + 5ix + -2iy + -2i2y + 7x + -2y = 5 + 6i + -5 + -6i

Reorder the terms:
-5 + -6i + 5ix + -2iy + -2i2y + 7x + -2y = 5 + -5 + 6i + -6i

Combine like terms: 5 + -5 = 0
-5 + -6i + 5ix + -2iy + -2i2y + 7x + -2y = 0 + 6i + -6i
-5 + -6i + 5ix + -2iy + -2i2y + 7x + -2y = 6i + -6i

Combine like terms: 6i + -6i = 0
-5 + -6i + 5ix + -2iy + -2i2y + 7x + -2y = 0

The solution to this equation could not be determined.

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