(2+3i)(x-iy)=3(x-2iy)+(2+i)

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


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

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

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

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

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

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

Remove parenthesis around (2 + i)
3ix + -2iy + -3i2y + 2x = -6iy + 3x + 2 + i

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

Solving
3ix + -2iy + -3i2y + 2x = 2 + i + -6iy + 3x

Solving for variable 'i'.

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

Combine like terms: -2iy + 6iy = 4iy
-2 + -1i + 3ix + 4iy + -3i2y + 2x + -3x = 2 + i + -6iy + 3x + -2 + -1i + 6iy + -3x

Combine like terms: 2x + -3x = -1x
-2 + -1i + 3ix + 4iy + -3i2y + -1x = 2 + i + -6iy + 3x + -2 + -1i + 6iy + -3x

Reorder the terms:
-2 + -1i + 3ix + 4iy + -3i2y + -1x = 2 + -2 + i + -1i + -6iy + 6iy + 3x + -3x

Combine like terms: 2 + -2 = 0
-2 + -1i + 3ix + 4iy + -3i2y + -1x = 0 + i + -1i + -6iy + 6iy + 3x + -3x
-2 + -1i + 3ix + 4iy + -3i2y + -1x = i + -1i + -6iy + 6iy + 3x + -3x

Combine like terms: i + -1i = 0
-2 + -1i + 3ix + 4iy + -3i2y + -1x = 0 + -6iy + 6iy + 3x + -3x
-2 + -1i + 3ix + 4iy + -3i2y + -1x = -6iy + 6iy + 3x + -3x

Combine like terms: -6iy + 6iy = 0
-2 + -1i + 3ix + 4iy + -3i2y + -1x = 0 + 3x + -3x
-2 + -1i + 3ix + 4iy + -3i2y + -1x = 3x + -3x

Combine like terms: 3x + -3x = 0
-2 + -1i + 3ix + 4iy + -3i2y + -1x = 0

The solution to this equation could not be determined.

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