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

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


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

Reorder the terms:
(x + 2y)(-1i + y) = -4 + -7i

Multiply (x + 2y) * (-1i + y)
(x(-1i + y) + 2y * (-1i + y)) = -4 + -7i
((-1i * x + y * x) + 2y * (-1i + y)) = -4 + -7i
((-1ix + xy) + 2y * (-1i + y)) = -4 + -7i
(-1ix + xy + (-1i * 2y + y * 2y)) = -4 + -7i
(-1ix + xy + (-2iy + 2y2)) = -4 + -7i

Reorder the terms:
(-1ix + -2iy + xy + 2y2) = -4 + -7i
(-1ix + -2iy + xy + 2y2) = -4 + -7i

Solving
-1ix + -2iy + xy + 2y2 = -4 + -7i

Solving for variable 'i'.

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

Add '7i' to each side of the equation.
-1ix + -2iy + xy + 7i + 2y2 = -4 + -7i + 7i

Reorder the terms:
7i + -1ix + -2iy + xy + 2y2 = -4 + -7i + 7i

Combine like terms: -7i + 7i = 0
7i + -1ix + -2iy + xy + 2y2 = -4 + 0
7i + -1ix + -2iy + xy + 2y2 = -4

Add '-1xy' to each side of the equation.
7i + -1ix + -2iy + xy + -1xy + 2y2 = -4 + -1xy

Combine like terms: xy + -1xy = 0
7i + -1ix + -2iy + 0 + 2y2 = -4 + -1xy
7i + -1ix + -2iy + 2y2 = -4 + -1xy

Add '-2y2' to each side of the equation.
7i + -1ix + -2iy + 2y2 + -2y2 = -4 + -1xy + -2y2

Combine like terms: 2y2 + -2y2 = 0
7i + -1ix + -2iy + 0 = -4 + -1xy + -2y2
7i + -1ix + -2iy = -4 + -1xy + -2y2

Reorder the terms:
4 + 7i + -1ix + -2iy + xy + 2y2 = -4 + -1xy + -2y2 + 4 + xy + 2y2

Reorder the terms:
4 + 7i + -1ix + -2iy + xy + 2y2 = -4 + 4 + -1xy + xy + -2y2 + 2y2

Combine like terms: -4 + 4 = 0
4 + 7i + -1ix + -2iy + xy + 2y2 = 0 + -1xy + xy + -2y2 + 2y2
4 + 7i + -1ix + -2iy + xy + 2y2 = -1xy + xy + -2y2 + 2y2

Combine like terms: -1xy + xy = 0
4 + 7i + -1ix + -2iy + xy + 2y2 = 0 + -2y2 + 2y2
4 + 7i + -1ix + -2iy + xy + 2y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
4 + 7i + -1ix + -2iy + xy + 2y2 = 0

The solution to this equation could not be determined.

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