[(y)-2x][2x+(y)]=

Solution for [(y)-2x][2x+(y)]= equation:

Simplifying
[(y) + -2x][2x + (y)] = 0
[y + -2x][2x + (y)] = 0

Reorder the terms:
[-2x + y][2x + (y)] = 0
[-2x + y][2x + y] = 0

Multiply [-2x + y] * [2x + y]
[-2x * [2x + y] + y[2x + y]] = 0
[[2x * -2x + y * -2x] + y[2x + y]] = 0

Reorder the terms:
[[-2xy + -4x2] + y[2x + y]] = 0
[[-2xy + -4x2] + y[2x + y]] = 0
[-2xy + -4x2 + [2x * y + y * y]] = 0
[-2xy + -4x2 + [2xy + y2]] = 0

Reorder the terms:
[-2xy + 2xy + -4x2 + y2] = 0

Combine like terms: -2xy + 2xy = 0
[0 + -4x2 + y2] = 0
[-4x2 + y2] = 0

Solving
-4x2 + y2 = 0

Solving for variable 'x'.

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

Add '-1y2' to each side of the equation.
-4x2 + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
-4x2 + 0 = 0 + -1y2
-4x2 = 0 + -1y2
Remove the zero:
-4x2 = -1y2

Divide each side by '-4'.
x2 = 0.25y2

Simplifying
x2 = 0.25y2

Take the square root of each side:
x = {-0.5y, 0.5y}