(X+yi)+(3+2i)=(4-6i)+(3x-yi)

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Solution for (X+yi)+(3+2i)=(4-6i)+(3x-yi) equation: 


Simplifying
(X + yi) + (3 + 2i) = (4 + -6i) + (3x + -1yi)

Remove parenthesis around (X + iy)
X + iy + (3 + 2i) = (4 + -6i) + (3x + -1yi)

Remove parenthesis around (3 + 2i)
X + iy + 3 + 2i = (4 + -6i) + (3x + -1yi)

Reorder the terms:
3 + X + 2i + iy = (4 + -6i) + (3x + -1yi)

Remove parenthesis around (4 + -6i)
3 + X + 2i + iy = 4 + -6i + (3x + -1yi)

Reorder the terms:
3 + X + 2i + iy = 4 + -6i + (-1iy + 3x)

Remove parenthesis around (-1iy + 3x)
3 + X + 2i + iy = 4 + -6i + -1iy + 3x

Solving
3 + X + 2i + iy = 4 + -6i + -1iy + 3x

Solving for variable 'X'.

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

Add '-3' to each side of the equation.
3 + X + 2i + -3 + iy = 4 + -6i + -1iy + -3 + 3x

Reorder the terms:
3 + -3 + X + 2i + iy = 4 + -6i + -1iy + -3 + 3x

Combine like terms: 3 + -3 = 0
0 + X + 2i + iy = 4 + -6i + -1iy + -3 + 3x
X + 2i + iy = 4 + -6i + -1iy + -3 + 3x

Reorder the terms:
X + 2i + iy = 4 + -3 + -6i + -1iy + 3x

Combine like terms: 4 + -3 = 1
X + 2i + iy = 1 + -6i + -1iy + 3x

Add '-2i' to each side of the equation.
X + 2i + -2i + iy = 1 + -6i + -1iy + -2i + 3x

Combine like terms: 2i + -2i = 0
X + 0 + iy = 1 + -6i + -1iy + -2i + 3x
X + iy = 1 + -6i + -1iy + -2i + 3x

Reorder the terms:
X + iy = 1 + -6i + -2i + -1iy + 3x

Combine like terms: -6i + -2i = -8i
X + iy = 1 + -8i + -1iy + 3x

Add '-1iy' to each side of the equation.
X + iy + -1iy = 1 + -8i + -1iy + -1iy + 3x

Combine like terms: iy + -1iy = 0
X + 0 = 1 + -8i + -1iy + -1iy + 3x
X = 1 + -8i + -1iy + -1iy + 3x

Combine like terms: -1iy + -1iy = -2iy
X = 1 + -8i + -2iy + 3x

Simplifying
X = 1 + -8i + -2iy + 3x

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