(x+y)(x-y)+2(x^2+Y^2)=0

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Solution for (x+y)(x-y)+2(x^2+Y^2)=0 equation: 


Simplifying
(x + y)(x + -1y) + 2(x2 + Y2) = 0

Multiply (x + y) * (x + -1y)
(x(x + -1y) + y(x + -1y)) + 2(x2 + Y2) = 0
((x * x + -1y * x) + y(x + -1y)) + 2(x2 + Y2) = 0

Reorder the terms:
((-1xy + x2) + y(x + -1y)) + 2(x2 + Y2) = 0
((-1xy + x2) + y(x + -1y)) + 2(x2 + Y2) = 0
(-1xy + x2 + (x * y + -1y * y)) + 2(x2 + Y2) = 0
(-1xy + x2 + (xy + -1y2)) + 2(x2 + Y2) = 0

Reorder the terms:
(-1xy + xy + x2 + -1y2) + 2(x2 + Y2) = 0

Combine like terms: -1xy + xy = 0
(0 + x2 + -1y2) + 2(x2 + Y2) = 0
(x2 + -1y2) + 2(x2 + Y2) = 0

Reorder the terms:
x2 + -1y2 + 2(Y2 + x2) = 0
x2 + -1y2 + (Y2 * 2 + x2 * 2) = 0
x2 + -1y2 + (2Y2 + 2x2) = 0

Reorder the terms:
2Y2 + x2 + 2x2 + -1y2 = 0

Combine like terms: x2 + 2x2 = 3x2
2Y2 + 3x2 + -1y2 = 0

Solving
2Y2 + 3x2 + -1y2 = 0

Solving for variable 'Y'.

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

Add '-3x2' to each side of the equation.
2Y2 + 3x2 + -3x2 + -1y2 = 0 + -3x2

Combine like terms: 3x2 + -3x2 = 0
2Y2 + 0 + -1y2 = 0 + -3x2
2Y2 + -1y2 = 0 + -3x2
Remove the zero:
2Y2 + -1y2 = -3x2

Add 'y2' to each side of the equation.
2Y2 + -1y2 + y2 = -3x2 + y2

Combine like terms: -1y2 + y2 = 0
2Y2 + 0 = -3x2 + y2
2Y2 = -3x2 + y2

Divide each side by '2'.
Y2 = -1.5x2 + 0.5y2

Simplifying
Y2 = -1.5x2 + 0.5y2

Reorder the terms:
Y2 + 1.5x2 + -0.5y2 = -1.5x2 + 1.5x2 + 0.5y2 + -0.5y2

Combine like terms: -1.5x2 + 1.5x2 = 0.0
Y2 + 1.5x2 + -0.5y2 = 0.0 + 0.5y2 + -0.5y2
Y2 + 1.5x2 + -0.5y2 = 0.5y2 + -0.5y2

Combine like terms: 0.5y2 + -0.5y2 = 0.0
Y2 + 1.5x2 + -0.5y2 = 0.0

The solution to this equation could not be determined.

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