(2x+3y)+(4x-7y)i=6-i

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Solution for (2x+3y)+(4x-7y)i=6-i equation: 


Simplifying
(2x + 3y) + (4x + -7y) * i = 6 + -1i

Remove parenthesis around (2x + 3y)
2x + 3y + (4x + -7y) * i = 6 + -1i

Reorder the terms for easier multiplication:
2x + 3y + i(4x + -7y) = 6 + -1i
2x + 3y + (4x * i + -7y * i) = 6 + -1i
2x + 3y + (4ix + -7iy) = 6 + -1i

Reorder the terms:
4ix + -7iy + 2x + 3y = 6 + -1i

Solving
4ix + -7iy + 2x + 3y = 6 + -1i

Solving for variable 'i'.

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

Add 'i' to each side of the equation.
4ix + -7iy + 2x + i + 3y = 6 + -1i + i

Reorder the terms:
i + 4ix + -7iy + 2x + 3y = 6 + -1i + i

Combine like terms: -1i + i = 0
i + 4ix + -7iy + 2x + 3y = 6 + 0
i + 4ix + -7iy + 2x + 3y = 6

Add '-2x' to each side of the equation.
i + 4ix + -7iy + 2x + -2x + 3y = 6 + -2x

Combine like terms: 2x + -2x = 0
i + 4ix + -7iy + 0 + 3y = 6 + -2x
i + 4ix + -7iy + 3y = 6 + -2x

Add '-3y' to each side of the equation.
i + 4ix + -7iy + 3y + -3y = 6 + -2x + -3y

Combine like terms: 3y + -3y = 0
i + 4ix + -7iy + 0 = 6 + -2x + -3y
i + 4ix + -7iy = 6 + -2x + -3y

Reorder the terms:
-6 + i + 4ix + -7iy + 2x + 3y = 6 + -2x + -3y + -6 + 2x + 3y

Reorder the terms:
-6 + i + 4ix + -7iy + 2x + 3y = 6 + -6 + -2x + 2x + -3y + 3y

Combine like terms: 6 + -6 = 0
-6 + i + 4ix + -7iy + 2x + 3y = 0 + -2x + 2x + -3y + 3y
-6 + i + 4ix + -7iy + 2x + 3y = -2x + 2x + -3y + 3y

Combine like terms: -2x + 2x = 0
-6 + i + 4ix + -7iy + 2x + 3y = 0 + -3y + 3y
-6 + i + 4ix + -7iy + 2x + 3y = -3y + 3y

Combine like terms: -3y + 3y = 0
-6 + i + 4ix + -7iy + 2x + 3y = 0

The solution to this equation could not be determined.

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