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

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


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

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

Multiply (-1i + 3x) * (2 + i)
(-1i * (2 + i) + 3x * (2 + i)) + (x + -1iy)(1 + 2i) = 5 + 6i
((2 * -1i + i * -1i) + 3x * (2 + i)) + (x + -1iy)(1 + 2i) = 5 + 6i
((-2i + -1i2) + 3x * (2 + i)) + (x + -1iy)(1 + 2i) = 5 + 6i
(-2i + -1i2 + (2 * 3x + i * 3x)) + (x + -1iy)(1 + 2i) = 5 + 6i

Reorder the terms:
(-2i + -1i2 + (3ix + 6x)) + (x + -1iy)(1 + 2i) = 5 + 6i
(-2i + -1i2 + (3ix + 6x)) + (x + -1iy)(1 + 2i) = 5 + 6i

Reorder the terms:
(-2i + 3ix + -1i2 + 6x) + (x + -1iy)(1 + 2i) = 5 + 6i
(-2i + 3ix + -1i2 + 6x) + (x + -1iy)(1 + 2i) = 5 + 6i

Reorder the terms:
-2i + 3ix + -1i2 + 6x + (-1iy + x)(1 + 2i) = 5 + 6i

Multiply (-1iy + x) * (1 + 2i)
-2i + 3ix + -1i2 + 6x + (-1iy * (1 + 2i) + x(1 + 2i)) = 5 + 6i
-2i + 3ix + -1i2 + 6x + ((1 * -1iy + 2i * -1iy) + x(1 + 2i)) = 5 + 6i
-2i + 3ix + -1i2 + 6x + ((-1iy + -2i2y) + x(1 + 2i)) = 5 + 6i
-2i + 3ix + -1i2 + 6x + (-1iy + -2i2y + (1 * x + 2i * x)) = 5 + 6i

Reorder the terms:
-2i + 3ix + -1i2 + 6x + (-1iy + -2i2y + (2ix + 1x)) = 5 + 6i
-2i + 3ix + -1i2 + 6x + (-1iy + -2i2y + (2ix + 1x)) = 5 + 6i

Reorder the terms:
-2i + 3ix + -1i2 + 6x + (2ix + -1iy + -2i2y + 1x) = 5 + 6i
-2i + 3ix + -1i2 + 6x + (2ix + -1iy + -2i2y + 1x) = 5 + 6i

Reorder the terms:
-2i + 3ix + 2ix + -1iy + -1i2 + -2i2y + 6x + 1x = 5 + 6i

Combine like terms: 3ix + 2ix = 5ix
-2i + 5ix + -1iy + -1i2 + -2i2y + 6x + 1x = 5 + 6i

Combine like terms: 6x + 1x = 7x
-2i + 5ix + -1iy + -1i2 + -2i2y + 7x = 5 + 6i

Solving
-2i + 5ix + -1iy + -1i2 + -2i2y + 7x = 5 + 6i

Solving for variable 'i'.

Reorder the terms:
-5 + -2i + -6i + 5ix + -1iy + -1i2 + -2i2y + 7x = 5 + 6i + -5 + -6i

Combine like terms: -2i + -6i = -8i
-5 + -8i + 5ix + -1iy + -1i2 + -2i2y + 7x = 5 + 6i + -5 + -6i

Reorder the terms:
-5 + -8i + 5ix + -1iy + -1i2 + -2i2y + 7x = 5 + -5 + 6i + -6i

Combine like terms: 5 + -5 = 0
-5 + -8i + 5ix + -1iy + -1i2 + -2i2y + 7x = 0 + 6i + -6i
-5 + -8i + 5ix + -1iy + -1i2 + -2i2y + 7x = 6i + -6i

Combine like terms: 6i + -6i = 0
-5 + -8i + 5ix + -1iy + -1i2 + -2i2y + 7x = 0

The solution to this equation could not be determined.

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