2x-3iy+4ix-2y-5-10i=x+y+2-i(y-x+3)

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Solution for 2x-3iy+4ix-2y-5-10i=x+y+2-i(y-x+3) equation: 


Simplifying
2x + -3iy + 4ix + -2y + -5 + -10i = x + y + 2 + -1i(y + -1x + 3)

Reorder the terms:
-5 + -10i + 4ix + -3iy + 2x + -2y = x + y + 2 + -1i(y + -1x + 3)

Reorder the terms:
-5 + -10i + 4ix + -3iy + 2x + -2y = x + y + 2 + -1i(3 + -1x + y)
-5 + -10i + 4ix + -3iy + 2x + -2y = x + y + 2 + (3 * -1i + -1x * -1i + y * -1i)
-5 + -10i + 4ix + -3iy + 2x + -2y = x + y + 2 + (-3i + 1ix + -1iy)

Reorder the terms:
-5 + -10i + 4ix + -3iy + 2x + -2y = 2 + -3i + 1ix + -1iy + x + y

Solving
-5 + -10i + 4ix + -3iy + 2x + -2y = 2 + -3i + 1ix + -1iy + x + y

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '3i' to each side of the equation.
-5 + -10i + 4ix + -3iy + 2x + 3i + -2y = 2 + -3i + 1ix + -1iy + x + 3i + y

Reorder the terms:
-5 + -10i + 3i + 4ix + -3iy + 2x + -2y = 2 + -3i + 1ix + -1iy + x + 3i + y

Combine like terms: -10i + 3i = -7i
-5 + -7i + 4ix + -3iy + 2x + -2y = 2 + -3i + 1ix + -1iy + x + 3i + y

Reorder the terms:
-5 + -7i + 4ix + -3iy + 2x + -2y = 2 + -3i + 3i + 1ix + -1iy + x + y

Combine like terms: -3i + 3i = 0
-5 + -7i + 4ix + -3iy + 2x + -2y = 2 + 0 + 1ix + -1iy + x + y
-5 + -7i + 4ix + -3iy + 2x + -2y = 2 + 1ix + -1iy + x + y

Add '-1ix' to each side of the equation.
-5 + -7i + 4ix + -3iy + 2x + -1ix + -2y = 2 + 1ix + -1iy + x + -1ix + y

Reorder the terms:
-5 + -7i + 4ix + -1ix + -3iy + 2x + -2y = 2 + 1ix + -1iy + x + -1ix + y

Combine like terms: 4ix + -1ix = 3ix
-5 + -7i + 3ix + -3iy + 2x + -2y = 2 + 1ix + -1iy + x + -1ix + y

Reorder the terms:
-5 + -7i + 3ix + -3iy + 2x + -2y = 2 + 1ix + -1ix + -1iy + x + y

Combine like terms: 1ix + -1ix = 0
-5 + -7i + 3ix + -3iy + 2x + -2y = 2 + 0 + -1iy + x + y
-5 + -7i + 3ix + -3iy + 2x + -2y = 2 + -1iy + x + y

Add 'iy' to each side of the equation.
-5 + -7i + 3ix + -3iy + 2x + iy + -2y = 2 + -1iy + x + iy + y

Reorder the terms:
-5 + -7i + 3ix + -3iy + iy + 2x + -2y = 2 + -1iy + x + iy + y

Combine like terms: -3iy + iy = -2iy
-5 + -7i + 3ix + -2iy + 2x + -2y = 2 + -1iy + x + iy + y

Reorder the terms:
-5 + -7i + 3ix + -2iy + 2x + -2y = 2 + -1iy + iy + x + y

Combine like terms: -1iy + iy = 0
-5 + -7i + 3ix + -2iy + 2x + -2y = 2 + 0 + x + y
-5 + -7i + 3ix + -2iy + 2x + -2y = 2 + x + y

Add '5' to each side of the equation.
-5 + -7i + 3ix + -2iy + 2x + 5 + -2y = 2 + x + 5 + y

Reorder the terms:
-5 + 5 + -7i + 3ix + -2iy + 2x + -2y = 2 + x + 5 + y

Combine like terms: -5 + 5 = 0
0 + -7i + 3ix + -2iy + 2x + -2y = 2 + x + 5 + y
-7i + 3ix + -2iy + 2x + -2y = 2 + x + 5 + y

Reorder the terms:
-7i + 3ix + -2iy + 2x + -2y = 2 + 5 + x + y

Combine like terms: 2 + 5 = 7
-7i + 3ix + -2iy + 2x + -2y = 7 + x + y

Add '-2x' to each side of the equation.
-7i + 3ix + -2iy + 2x + -2x + -2y = 7 + x + -2x + y

Combine like terms: 2x + -2x = 0
-7i + 3ix + -2iy + 0 + -2y = 7 + x + -2x + y
-7i + 3ix + -2iy + -2y = 7 + x + -2x + y

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

Add '2y' to each side of the equation.
-7i + 3ix + -2iy + -2y + 2y = 7 + -1x + y + 2y

Combine like terms: -2y + 2y = 0
-7i + 3ix + -2iy + 0 = 7 + -1x + y + 2y
-7i + 3ix + -2iy = 7 + -1x + y + 2y

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

Reorder the terms:
-7 + -7i + 3ix + -2iy + x + -3y = 7 + -1x + 3y + -7 + x + -3y

Reorder the terms:
-7 + -7i + 3ix + -2iy + x + -3y = 7 + -7 + -1x + x + 3y + -3y

Combine like terms: 7 + -7 = 0
-7 + -7i + 3ix + -2iy + x + -3y = 0 + -1x + x + 3y + -3y
-7 + -7i + 3ix + -2iy + x + -3y = -1x + x + 3y + -3y

Combine like terms: -1x + x = 0
-7 + -7i + 3ix + -2iy + x + -3y = 0 + 3y + -3y
-7 + -7i + 3ix + -2iy + x + -3y = 3y + -3y

Combine like terms: 3y + -3y = 0
-7 + -7i + 3ix + -2iy + x + -3y = 0

The solution to this equation could not be determined.

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