(x+yi)(3+2i)-(x+yi)=(9-2i)

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Solution for (x+yi)(3+2i)-(x+yi)=(9-2i) equation: 


Simplifying
(x + yi)(3 + 2i) + -1(x + yi) = (9 + -2i)

Reorder the terms:
(iy + x)(3 + 2i) + -1(x + yi) = (9 + -2i)

Multiply (iy + x) * (3 + 2i)
(iy(3 + 2i) + x(3 + 2i)) + -1(x + yi) = (9 + -2i)
((3 * iy + 2i * iy) + x(3 + 2i)) + -1(x + yi) = (9 + -2i)
((3iy + 2i2y) + x(3 + 2i)) + -1(x + yi) = (9 + -2i)
(3iy + 2i2y + (3 * x + 2i * x)) + -1(x + yi) = (9 + -2i)

Reorder the terms:
(3iy + 2i2y + (2ix + 3x)) + -1(x + yi) = (9 + -2i)
(3iy + 2i2y + (2ix + 3x)) + -1(x + yi) = (9 + -2i)

Reorder the terms:
(2ix + 3iy + 2i2y + 3x) + -1(x + yi) = (9 + -2i)
(2ix + 3iy + 2i2y + 3x) + -1(x + yi) = (9 + -2i)

Reorder the terms:
2ix + 3iy + 2i2y + 3x + -1(iy + x) = (9 + -2i)
2ix + 3iy + 2i2y + 3x + (iy * -1 + x * -1) = (9 + -2i)
2ix + 3iy + 2i2y + 3x + (-1iy + -1x) = (9 + -2i)

Reorder the terms:
2ix + 3iy + -1iy + 2i2y + 3x + -1x = (9 + -2i)

Combine like terms: 3iy + -1iy = 2iy
2ix + 2iy + 2i2y + 3x + -1x = (9 + -2i)

Combine like terms: 3x + -1x = 2x
2ix + 2iy + 2i2y + 2x = (9 + -2i)

Remove parenthesis around (9 + -2i)
2ix + 2iy + 2i2y + 2x = 9 + -2i

Solving
2ix + 2iy + 2i2y + 2x = 9 + -2i

Solving for variable 'i'.

Reorder the terms:
-9 + 2i + 2ix + 2iy + 2i2y + 2x = 9 + -2i + -9 + 2i

Reorder the terms:
-9 + 2i + 2ix + 2iy + 2i2y + 2x = 9 + -9 + -2i + 2i

Combine like terms: 9 + -9 = 0
-9 + 2i + 2ix + 2iy + 2i2y + 2x = 0 + -2i + 2i
-9 + 2i + 2ix + 2iy + 2i2y + 2x = -2i + 2i

Combine like terms: -2i + 2i = 0
-9 + 2i + 2ix + 2iy + 2i2y + 2x = 0

The solution to this equation could not be determined.

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