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

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


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

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

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

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

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

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

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

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

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

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

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

Remove parenthesis around (5 + 6i)
-2 + -1i + 5ix + -1iy + -2i2y + 7x = 5 + 6i

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

Solving for variable 'i'.

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

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

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

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

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

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

The solution to this equation could not be determined.

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