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

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


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

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

Multiply (iy + 4x) * (2 + -3i)
(iy(2 + -3i) + 4x * (2 + -3i)) = (-1x + y)(i + -3) + -1(3 + 4i)
((2 * iy + -3i * iy) + 4x * (2 + -3i)) = (-1x + y)(i + -3) + -1(3 + 4i)
((2iy + -3i2y) + 4x * (2 + -3i)) = (-1x + y)(i + -3) + -1(3 + 4i)
(2iy + -3i2y + (2 * 4x + -3i * 4x)) = (-1x + y)(i + -3) + -1(3 + 4i)

Reorder the terms:
(2iy + -3i2y + (-12ix + 8x)) = (-1x + y)(i + -3) + -1(3 + 4i)
(2iy + -3i2y + (-12ix + 8x)) = (-1x + y)(i + -3) + -1(3 + 4i)

Reorder the terms:
(-12ix + 2iy + -3i2y + 8x) = (-1x + y)(i + -3) + -1(3 + 4i)
(-12ix + 2iy + -3i2y + 8x) = (-1x + y)(i + -3) + -1(3 + 4i)

Reorder the terms:
-12ix + 2iy + -3i2y + 8x = (-1x + y)(-3 + i) + -1(3 + 4i)

Multiply (-1x + y) * (-3 + i)
-12ix + 2iy + -3i2y + 8x = (-1x * (-3 + i) + y(-3 + i)) + -1(3 + 4i)
-12ix + 2iy + -3i2y + 8x = ((-3 * -1x + i * -1x) + y(-3 + i)) + -1(3 + 4i)

Reorder the terms:
-12ix + 2iy + -3i2y + 8x = ((-1ix + 3x) + y(-3 + i)) + -1(3 + 4i)
-12ix + 2iy + -3i2y + 8x = ((-1ix + 3x) + y(-3 + i)) + -1(3 + 4i)
-12ix + 2iy + -3i2y + 8x = (-1ix + 3x + (-3 * y + i * y)) + -1(3 + 4i)

Reorder the terms:
-12ix + 2iy + -3i2y + 8x = (-1ix + 3x + (iy + -3y)) + -1(3 + 4i)
-12ix + 2iy + -3i2y + 8x = (-1ix + 3x + (iy + -3y)) + -1(3 + 4i)

Reorder the terms:
-12ix + 2iy + -3i2y + 8x = (-1ix + iy + 3x + -3y) + -1(3 + 4i)
-12ix + 2iy + -3i2y + 8x = (-1ix + iy + 3x + -3y) + -1(3 + 4i)
-12ix + 2iy + -3i2y + 8x = -1ix + iy + 3x + -3y + (3 * -1 + 4i * -1)
-12ix + 2iy + -3i2y + 8x = -1ix + iy + 3x + -3y + (-3 + -4i)

Reorder the terms:
-12ix + 2iy + -3i2y + 8x = -3 + -4i + -1ix + iy + 3x + -3y

Solving
-12ix + 2iy + -3i2y + 8x = -3 + -4i + -1ix + iy + 3x + -3y

Solving for variable 'i'.

Reorder the terms:
3 + 4i + -12ix + ix + 2iy + -1iy + -3i2y + 8x + -3x + 3y = -3 + -4i + -1ix + iy + 3x + -3y + 3 + 4i + ix + -1iy + -3x + 3y

Combine like terms: -12ix + ix = -11ix
3 + 4i + -11ix + 2iy + -1iy + -3i2y + 8x + -3x + 3y = -3 + -4i + -1ix + iy + 3x + -3y + 3 + 4i + ix + -1iy + -3x + 3y

Combine like terms: 2iy + -1iy = 1iy
3 + 4i + -11ix + 1iy + -3i2y + 8x + -3x + 3y = -3 + -4i + -1ix + iy + 3x + -3y + 3 + 4i + ix + -1iy + -3x + 3y

Combine like terms: 8x + -3x = 5x
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = -3 + -4i + -1ix + iy + 3x + -3y + 3 + 4i + ix + -1iy + -3x + 3y

Reorder the terms:
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = -3 + 3 + -4i + 4i + -1ix + ix + iy + -1iy + 3x + -3x + -3y + 3y

Combine like terms: -3 + 3 = 0
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = 0 + -4i + 4i + -1ix + ix + iy + -1iy + 3x + -3x + -3y + 3y
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = -4i + 4i + -1ix + ix + iy + -1iy + 3x + -3x + -3y + 3y

Combine like terms: -4i + 4i = 0
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = 0 + -1ix + ix + iy + -1iy + 3x + -3x + -3y + 3y
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = -1ix + ix + iy + -1iy + 3x + -3x + -3y + 3y

Combine like terms: -1ix + ix = 0
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = 0 + iy + -1iy + 3x + -3x + -3y + 3y
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = iy + -1iy + 3x + -3x + -3y + 3y

Combine like terms: iy + -1iy = 0
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = 0 + 3x + -3x + -3y + 3y
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = 3x + -3x + -3y + 3y

Combine like terms: 3x + -3x = 0
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = 0 + -3y + 3y
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = -3y + 3y

Combine like terms: -3y + 3y = 0
3 + 4i + -11ix + 1iy + -3i2y + 5x + 3y = 0

The solution to this equation could not be determined.

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