(2+3i)*x+(5y-2i)*(3-i)=3*x-4i

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Solution for (2+3i)*x+(5y-2i)*(3-i)=3*x-4i equation: 


Simplifying
(2 + 3i) * x + (5y + -2i)(3 + -1i) = 3x + -4i

Reorder the terms for easier multiplication:
x(2 + 3i) + (5y + -2i)(3 + -1i) = 3x + -4i
(2 * x + 3i * x) + (5y + -2i)(3 + -1i) = 3x + -4i

Reorder the terms:
(3ix + 2x) + (5y + -2i)(3 + -1i) = 3x + -4i
(3ix + 2x) + (5y + -2i)(3 + -1i) = 3x + -4i

Reorder the terms:
3ix + 2x + (-2i + 5y)(3 + -1i) = 3x + -4i

Multiply (-2i + 5y) * (3 + -1i)
3ix + 2x + (-2i * (3 + -1i) + 5y * (3 + -1i)) = 3x + -4i
3ix + 2x + ((3 * -2i + -1i * -2i) + 5y * (3 + -1i)) = 3x + -4i
3ix + 2x + ((-6i + 2i2) + 5y * (3 + -1i)) = 3x + -4i
3ix + 2x + (-6i + 2i2 + (3 * 5y + -1i * 5y)) = 3x + -4i

Reorder the terms:
3ix + 2x + (-6i + 2i2 + (-5iy + 15y)) = 3x + -4i
3ix + 2x + (-6i + 2i2 + (-5iy + 15y)) = 3x + -4i

Reorder the terms:
3ix + 2x + (-6i + -5iy + 2i2 + 15y) = 3x + -4i
3ix + 2x + (-6i + -5iy + 2i2 + 15y) = 3x + -4i

Reorder the terms:
-6i + 3ix + -5iy + 2i2 + 2x + 15y = 3x + -4i

Reorder the terms:
-6i + 3ix + -5iy + 2i2 + 2x + 15y = -4i + 3x

Solving
-6i + 3ix + -5iy + 2i2 + 2x + 15y = -4i + 3x

Solving for variable 'i'.

Reorder the terms:
-6i + 4i + 3ix + -5iy + 2i2 + 2x + -3x + 15y = -4i + 3x + 4i + -3x

Combine like terms: -6i + 4i = -2i
-2i + 3ix + -5iy + 2i2 + 2x + -3x + 15y = -4i + 3x + 4i + -3x

Combine like terms: 2x + -3x = -1x
-2i + 3ix + -5iy + 2i2 + -1x + 15y = -4i + 3x + 4i + -3x

Reorder the terms:
-2i + 3ix + -5iy + 2i2 + -1x + 15y = -4i + 4i + 3x + -3x

Combine like terms: -4i + 4i = 0
-2i + 3ix + -5iy + 2i2 + -1x + 15y = 0 + 3x + -3x
-2i + 3ix + -5iy + 2i2 + -1x + 15y = 3x + -3x

Combine like terms: 3x + -3x = 0
-2i + 3ix + -5iy + 2i2 + -1x + 15y = 0

The solution to this equation could not be determined.

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