(x+yi)(3-2i)=x(x-4i)+iy^2

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


Simplifying
(x + yi)(3 + -2i) = x(x + -4i) + iy2

Reorder the terms:
(iy + x)(3 + -2i) = x(x + -4i) + iy2

Multiply (iy + x) * (3 + -2i)
(iy(3 + -2i) + x(3 + -2i)) = x(x + -4i) + iy2
((3 * iy + -2i * iy) + x(3 + -2i)) = x(x + -4i) + iy2
((3iy + -2i2y) + x(3 + -2i)) = x(x + -4i) + iy2
(3iy + -2i2y + (3 * x + -2i * x)) = x(x + -4i) + iy2

Reorder the terms:
(3iy + -2i2y + (-2ix + 3x)) = x(x + -4i) + iy2
(3iy + -2i2y + (-2ix + 3x)) = x(x + -4i) + iy2

Reorder the terms:
(-2ix + 3iy + -2i2y + 3x) = x(x + -4i) + iy2
(-2ix + 3iy + -2i2y + 3x) = x(x + -4i) + iy2

Reorder the terms:
-2ix + 3iy + -2i2y + 3x = x(-4i + x) + iy2
-2ix + 3iy + -2i2y + 3x = (-4i * x + x * x) + iy2
-2ix + 3iy + -2i2y + 3x = (-4ix + x2) + iy2

Reorder the terms:
-2ix + 3iy + -2i2y + 3x = -4ix + iy2 + x2

Solving
-2ix + 3iy + -2i2y + 3x = -4ix + iy2 + x2

Solving for variable 'i'.

Reorder the terms:
-2ix + 4ix + 3iy + -1iy2 + -2i2y + 3x + -1x2 = -4ix + iy2 + x2 + 4ix + -1iy2 + -1x2

Combine like terms: -2ix + 4ix = 2ix
2ix + 3iy + -1iy2 + -2i2y + 3x + -1x2 = -4ix + iy2 + x2 + 4ix + -1iy2 + -1x2

Reorder the terms:
2ix + 3iy + -1iy2 + -2i2y + 3x + -1x2 = -4ix + 4ix + iy2 + -1iy2 + x2 + -1x2

Combine like terms: -4ix + 4ix = 0
2ix + 3iy + -1iy2 + -2i2y + 3x + -1x2 = 0 + iy2 + -1iy2 + x2 + -1x2
2ix + 3iy + -1iy2 + -2i2y + 3x + -1x2 = iy2 + -1iy2 + x2 + -1x2

Combine like terms: iy2 + -1iy2 = 0
2ix + 3iy + -1iy2 + -2i2y + 3x + -1x2 = 0 + x2 + -1x2
2ix + 3iy + -1iy2 + -2i2y + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2ix + 3iy + -1iy2 + -2i2y + 3x + -1x2 = 0

The solution to this equation could not be determined.

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