(2+x-iy)=(1+2i)(3x+iy)

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Solution for (2+x-iy)=(1+2i)(3x+iy) equation: 


Simplifying
(2 + x + -1iy) = (1 + 2i)(3x + iy)

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

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

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

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

Reorder the terms:
2 + -1iy + x = (1iy + 3x + (6ix + 2i2y))
2 + -1iy + x = (1iy + 3x + (6ix + 2i2y))

Reorder the terms:
2 + -1iy + x = (6ix + 1iy + 2i2y + 3x)
2 + -1iy + x = (6ix + 1iy + 2i2y + 3x)

Solving
2 + -1iy + x = 6ix + 1iy + 2i2y + 3x

Solving for variable 'i'.

Reorder the terms:
2 + -6ix + -1iy + -1iy + -2i2y + x + -3x = 6ix + 1iy + 2i2y + 3x + -6ix + -1iy + -2i2y + -3x

Combine like terms: -1iy + -1iy = -2iy
2 + -6ix + -2iy + -2i2y + x + -3x = 6ix + 1iy + 2i2y + 3x + -6ix + -1iy + -2i2y + -3x

Combine like terms: x + -3x = -2x
2 + -6ix + -2iy + -2i2y + -2x = 6ix + 1iy + 2i2y + 3x + -6ix + -1iy + -2i2y + -3x

Reorder the terms:
2 + -6ix + -2iy + -2i2y + -2x = 6ix + -6ix + 1iy + -1iy + 2i2y + -2i2y + 3x + -3x

Combine like terms: 6ix + -6ix = 0
2 + -6ix + -2iy + -2i2y + -2x = 0 + 1iy + -1iy + 2i2y + -2i2y + 3x + -3x
2 + -6ix + -2iy + -2i2y + -2x = 1iy + -1iy + 2i2y + -2i2y + 3x + -3x

Combine like terms: 1iy + -1iy = 0
2 + -6ix + -2iy + -2i2y + -2x = 0 + 2i2y + -2i2y + 3x + -3x
2 + -6ix + -2iy + -2i2y + -2x = 2i2y + -2i2y + 3x + -3x

Combine like terms: 2i2y + -2i2y = 0
2 + -6ix + -2iy + -2i2y + -2x = 0 + 3x + -3x
2 + -6ix + -2iy + -2i2y + -2x = 3x + -3x

Combine like terms: 3x + -3x = 0
2 + -6ix + -2iy + -2i2y + -2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -3ix + -1iy + -1i2y + -1x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -3ix + -1iy + -1i2y + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -3ix + -1iy + -1i2y + -1x = 0

Solving
1 + -3ix + -1iy + -1i2y + -1x = 0

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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