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

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


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

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

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

Reorder the terms:
(-2iy + -2x + (4ix + 4i2y)) + 3(x + yi) = 4(2 + i)
(-2iy + -2x + (4ix + 4i2y)) + 3(x + yi) = 4(2 + i)

Reorder the terms:
(4ix + -2iy + 4i2y + -2x) + 3(x + yi) = 4(2 + i)
(4ix + -2iy + 4i2y + -2x) + 3(x + yi) = 4(2 + i)

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

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

Combine like terms: -2iy + 3iy = 1iy
4ix + 1iy + 4i2y + -2x + 3x = 4(2 + i)

Combine like terms: -2x + 3x = 1x
4ix + 1iy + 4i2y + 1x = 4(2 + i)
4ix + 1iy + 4i2y + 1x = (2 * 4 + i * 4)
4ix + 1iy + 4i2y + 1x = (8 + 4i)

Solving
4ix + 1iy + 4i2y + 1x = 8 + 4i

Solving for variable 'i'.

Reorder the terms:
-8 + -4i + 4ix + 1iy + 4i2y + 1x = 8 + 4i + -8 + -4i

Reorder the terms:
-8 + -4i + 4ix + 1iy + 4i2y + 1x = 8 + -8 + 4i + -4i

Combine like terms: 8 + -8 = 0
-8 + -4i + 4ix + 1iy + 4i2y + 1x = 0 + 4i + -4i
-8 + -4i + 4ix + 1iy + 4i2y + 1x = 4i + -4i

Combine like terms: 4i + -4i = 0
-8 + -4i + 4ix + 1iy + 4i2y + 1x = 0

The solution to this equation could not be determined.

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