(3-2i)(x+iy)=(2x-4iy)+(-1+2i)

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Solution for (3-2i)(x+iy)=(2x-4iy)+(-1+2i) equation: 


Simplifying
(3 + -2i)(x + iy) = (2x + -4iy) + (-1 + 2i)

Reorder the terms:
(3 + -2i)(iy + x) = (2x + -4iy) + (-1 + 2i)

Multiply (3 + -2i) * (iy + x)
(3(iy + x) + -2i * (iy + x)) = (2x + -4iy) + (-1 + 2i)
((iy * 3 + x * 3) + -2i * (iy + x)) = (2x + -4iy) + (-1 + 2i)
((3iy + 3x) + -2i * (iy + x)) = (2x + -4iy) + (-1 + 2i)
(3iy + 3x + (iy * -2i + x * -2i)) = (2x + -4iy) + (-1 + 2i)

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

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

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

Remove parenthesis around (-4iy + 2x)
-2ix + 3iy + -2i2y + 3x = -4iy + 2x + (-1 + 2i)

Remove parenthesis around (-1 + 2i)
-2ix + 3iy + -2i2y + 3x = -4iy + 2x + -1 + 2i

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

Solving
-2ix + 3iy + -2i2y + 3x = -1 + 2i + -4iy + 2x

Solving for variable 'i'.

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

Combine like terms: 3iy + 4iy = 7iy
1 + -2i + -2ix + 7iy + -2i2y + 3x + -2x = -1 + 2i + -4iy + 2x + 1 + -2i + 4iy + -2x

Combine like terms: 3x + -2x = 1x
1 + -2i + -2ix + 7iy + -2i2y + 1x = -1 + 2i + -4iy + 2x + 1 + -2i + 4iy + -2x

Reorder the terms:
1 + -2i + -2ix + 7iy + -2i2y + 1x = -1 + 1 + 2i + -2i + -4iy + 4iy + 2x + -2x

Combine like terms: -1 + 1 = 0
1 + -2i + -2ix + 7iy + -2i2y + 1x = 0 + 2i + -2i + -4iy + 4iy + 2x + -2x
1 + -2i + -2ix + 7iy + -2i2y + 1x = 2i + -2i + -4iy + 4iy + 2x + -2x

Combine like terms: 2i + -2i = 0
1 + -2i + -2ix + 7iy + -2i2y + 1x = 0 + -4iy + 4iy + 2x + -2x
1 + -2i + -2ix + 7iy + -2i2y + 1x = -4iy + 4iy + 2x + -2x

Combine like terms: -4iy + 4iy = 0
1 + -2i + -2ix + 7iy + -2i2y + 1x = 0 + 2x + -2x
1 + -2i + -2ix + 7iy + -2i2y + 1x = 2x + -2x

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

The solution to this equation could not be determined.

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