(3x-i)(2+4i)+(x-iy)(1+2i)=5-2i

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Solution for (3x-i)(2+4i)+(x-iy)(1+2i)=5-2i equation: 


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

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

Multiply (-1i + 3x) * (2 + 4i)
(-1i * (2 + 4i) + 3x * (2 + 4i)) + (x + -1iy)(1 + 2i) = 5 + -2i
((2 * -1i + 4i * -1i) + 3x * (2 + 4i)) + (x + -1iy)(1 + 2i) = 5 + -2i
((-2i + -4i2) + 3x * (2 + 4i)) + (x + -1iy)(1 + 2i) = 5 + -2i
(-2i + -4i2 + (2 * 3x + 4i * 3x)) + (x + -1iy)(1 + 2i) = 5 + -2i

Reorder the terms:
(-2i + -4i2 + (12ix + 6x)) + (x + -1iy)(1 + 2i) = 5 + -2i
(-2i + -4i2 + (12ix + 6x)) + (x + -1iy)(1 + 2i) = 5 + -2i

Reorder the terms:
(-2i + 12ix + -4i2 + 6x) + (x + -1iy)(1 + 2i) = 5 + -2i
(-2i + 12ix + -4i2 + 6x) + (x + -1iy)(1 + 2i) = 5 + -2i

Reorder the terms:
-2i + 12ix + -4i2 + 6x + (-1iy + x)(1 + 2i) = 5 + -2i

Multiply (-1iy + x) * (1 + 2i)
-2i + 12ix + -4i2 + 6x + (-1iy * (1 + 2i) + x(1 + 2i)) = 5 + -2i
-2i + 12ix + -4i2 + 6x + ((1 * -1iy + 2i * -1iy) + x(1 + 2i)) = 5 + -2i
-2i + 12ix + -4i2 + 6x + ((-1iy + -2i2y) + x(1 + 2i)) = 5 + -2i
-2i + 12ix + -4i2 + 6x + (-1iy + -2i2y + (1 * x + 2i * x)) = 5 + -2i

Reorder the terms:
-2i + 12ix + -4i2 + 6x + (-1iy + -2i2y + (2ix + 1x)) = 5 + -2i
-2i + 12ix + -4i2 + 6x + (-1iy + -2i2y + (2ix + 1x)) = 5 + -2i

Reorder the terms:
-2i + 12ix + -4i2 + 6x + (2ix + -1iy + -2i2y + 1x) = 5 + -2i
-2i + 12ix + -4i2 + 6x + (2ix + -1iy + -2i2y + 1x) = 5 + -2i

Reorder the terms:
-2i + 12ix + 2ix + -1iy + -4i2 + -2i2y + 6x + 1x = 5 + -2i

Combine like terms: 12ix + 2ix = 14ix
-2i + 14ix + -1iy + -4i2 + -2i2y + 6x + 1x = 5 + -2i

Combine like terms: 6x + 1x = 7x
-2i + 14ix + -1iy + -4i2 + -2i2y + 7x = 5 + -2i

Add '2i' to each side of the equation.
-2i + 14ix + -1iy + -4i2 + -2i2y + 2i + 7x = 5 + -2i + 2i

Reorder the terms:
-2i + 2i + 14ix + -1iy + -4i2 + -2i2y + 7x = 5 + -2i + 2i

Combine like terms: -2i + 2i = 0
0 + 14ix + -1iy + -4i2 + -2i2y + 7x = 5 + -2i + 2i
14ix + -1iy + -4i2 + -2i2y + 7x = 5 + -2i + 2i

Combine like terms: -2i + 2i = 0
14ix + -1iy + -4i2 + -2i2y + 7x = 5 + 0
14ix + -1iy + -4i2 + -2i2y + 7x = 5

Solving
14ix + -1iy + -4i2 + -2i2y + 7x = 5

Solving for variable 'i'.

Reorder the terms:
-5 + 14ix + -1iy + -4i2 + -2i2y + 7x = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 14ix + -1iy + -4i2 + -2i2y + 7x = 0

The solution to this equation could not be determined.

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