3(x+iy)=8-6i-(x-iy)

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Solution for 3(x+iy)=8-6i-(x-iy) equation:


Simplifying
3(x + iy) = 8 + -6i + -1(x + -1iy)

Reorder the terms:
3(iy + x) = 8 + -6i + -1(x + -1iy)
(iy * 3 + x * 3) = 8 + -6i + -1(x + -1iy)
(3iy + 3x) = 8 + -6i + -1(x + -1iy)

Reorder the terms:
3iy + 3x = 8 + -6i + -1(-1iy + x)
3iy + 3x = 8 + -6i + (-1iy * -1 + x * -1)
3iy + 3x = 8 + -6i + (1iy + -1x)

Solving
3iy + 3x = 8 + -6i + 1iy + -1x

Solving for variable 'i'.

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

Add '6i' to each side of the equation.
3iy + 6i + 3x = 8 + -6i + 1iy + 6i + -1x

Reorder the terms:
6i + 3iy + 3x = 8 + -6i + 1iy + 6i + -1x

Reorder the terms:
6i + 3iy + 3x = 8 + -6i + 6i + 1iy + -1x

Combine like terms: -6i + 6i = 0
6i + 3iy + 3x = 8 + 0 + 1iy + -1x
6i + 3iy + 3x = 8 + 1iy + -1x

Add '-1iy' to each side of the equation.
6i + 3iy + -1iy + 3x = 8 + 1iy + -1iy + -1x

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

Combine like terms: 1iy + -1iy = 0
6i + 2iy + 3x = 8 + 0 + -1x
6i + 2iy + 3x = 8 + -1x

Add '-3x' to each side of the equation.
6i + 2iy + 3x + -3x = 8 + -1x + -3x

Combine like terms: 3x + -3x = 0
6i + 2iy + 0 = 8 + -1x + -3x
6i + 2iy = 8 + -1x + -3x

Combine like terms: -1x + -3x = -4x
6i + 2iy = 8 + -4x

Reorder the terms:
-8 + 6i + 2iy + 4x = 8 + -4x + -8 + 4x

Reorder the terms:
-8 + 6i + 2iy + 4x = 8 + -8 + -4x + 4x

Combine like terms: 8 + -8 = 0
-8 + 6i + 2iy + 4x = 0 + -4x + 4x
-8 + 6i + 2iy + 4x = -4x + 4x

Combine like terms: -4x + 4x = 0
-8 + 6i + 2iy + 4x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3i + iy + 2x) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + 3i + iy + 2x)' equal to zero and attempt to solve: Simplifying -4 + 3i + iy + 2x = 0 Solving -4 + 3i + iy + 2x = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 3i + iy + 4 + 2x = 0 + 4 Reorder the terms: -4 + 4 + 3i + iy + 2x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3i + iy + 2x = 0 + 4 3i + iy + 2x = 0 + 4 Combine like terms: 0 + 4 = 4 3i + iy + 2x = 4 Add '-2x' to each side of the equation. 3i + iy + 2x + -2x = 4 + -2x Combine like terms: 2x + -2x = 0 3i + iy + 0 = 4 + -2x 3i + iy = 4 + -2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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