(y+2x)-(y-2x)(y+2x)=(y+2x)(1-y-2x)

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Solution for (y+2x)-(y-2x)(y+2x)=(y+2x)(1-y-2x) equation: 


Simplifying
(y + 2x) + -1(y + -2x)(y + 2x) = (y + 2x)(1 + -1y + -2x)

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

Remove parenthesis around (2x + y)
2x + y + -1(y + -2x)(y + 2x) = (y + 2x)(1 + -1y + -2x)

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

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

Multiply (-2x + y) * (2x + y)
2x + y + -1(-2x * (2x + y) + y(2x + y)) = (y + 2x)(1 + -1y + -2x)
2x + y + -1((2x * -2x + y * -2x) + y(2x + y)) = (y + 2x)(1 + -1y + -2x)

Reorder the terms:
2x + y + -1((-2xy + -4x2) + y(2x + y)) = (y + 2x)(1 + -1y + -2x)
2x + y + -1((-2xy + -4x2) + y(2x + y)) = (y + 2x)(1 + -1y + -2x)
2x + y + -1(-2xy + -4x2 + (2x * y + y * y)) = (y + 2x)(1 + -1y + -2x)
2x + y + -1(-2xy + -4x2 + (2xy + y2)) = (y + 2x)(1 + -1y + -2x)

Reorder the terms:
2x + y + -1(-2xy + 2xy + -4x2 + y2) = (y + 2x)(1 + -1y + -2x)

Combine like terms: -2xy + 2xy = 0
2x + y + -1(0 + -4x2 + y2) = (y + 2x)(1 + -1y + -2x)
2x + y + -1(-4x2 + y2) = (y + 2x)(1 + -1y + -2x)
2x + y + (-4x2 * -1 + y2 * -1) = (y + 2x)(1 + -1y + -2x)
2x + y + (4x2 + -1y2) = (y + 2x)(1 + -1y + -2x)

Reorder the terms:
2x + 4x2 + y + -1y2 = (y + 2x)(1 + -1y + -2x)

Reorder the terms:
2x + 4x2 + y + -1y2 = (2x + y)(1 + -1y + -2x)

Reorder the terms:
2x + 4x2 + y + -1y2 = (2x + y)(1 + -2x + -1y)

Multiply (2x + y) * (1 + -2x + -1y)
2x + 4x2 + y + -1y2 = (2x * (1 + -2x + -1y) + y(1 + -2x + -1y))
2x + 4x2 + y + -1y2 = ((1 * 2x + -2x * 2x + -1y * 2x) + y(1 + -2x + -1y))

Reorder the terms:
2x + 4x2 + y + -1y2 = ((2x + -2xy + -4x2) + y(1 + -2x + -1y))
2x + 4x2 + y + -1y2 = ((2x + -2xy + -4x2) + y(1 + -2x + -1y))
2x + 4x2 + y + -1y2 = (2x + -2xy + -4x2 + (1 * y + -2x * y + -1y * y))

Reorder the terms:
2x + 4x2 + y + -1y2 = (2x + -2xy + -4x2 + (-2xy + 1y + -1y2))
2x + 4x2 + y + -1y2 = (2x + -2xy + -4x2 + (-2xy + 1y + -1y2))

Reorder the terms:
2x + 4x2 + y + -1y2 = (2x + -2xy + -2xy + -4x2 + 1y + -1y2)

Combine like terms: -2xy + -2xy = -4xy
2x + 4x2 + y + -1y2 = (2x + -4xy + -4x2 + 1y + -1y2)

Add '-2x' to each side of the equation.
2x + 4x2 + y + -2x + -1y2 = 2x + -4xy + -4x2 + 1y + -2x + -1y2

Reorder the terms:
2x + -2x + 4x2 + y + -1y2 = 2x + -4xy + -4x2 + 1y + -2x + -1y2

Combine like terms: 2x + -2x = 0
0 + 4x2 + y + -1y2 = 2x + -4xy + -4x2 + 1y + -2x + -1y2
4x2 + y + -1y2 = 2x + -4xy + -4x2 + 1y + -2x + -1y2

Reorder the terms:
4x2 + y + -1y2 = 2x + -2x + -4xy + -4x2 + 1y + -1y2

Combine like terms: 2x + -2x = 0
4x2 + y + -1y2 = 0 + -4xy + -4x2 + 1y + -1y2
4x2 + y + -1y2 = -4xy + -4x2 + 1y + -1y2

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

Combine like terms: -1y2 + y2 = 0
4x2 + y + 0 = -4xy + -4x2 + 1y + -1y2 + y2
4x2 + y = -4xy + -4x2 + 1y + -1y2 + y2

Combine like terms: -1y2 + y2 = 0
4x2 + y = -4xy + -4x2 + 1y + 0
4x2 + y = -4xy + -4x2 + 1y

Solving
4x2 + y = -4xy + -4x2 + 1y

Solving for variable 'x'.

Reorder the terms:
4xy + 4x2 + 4x2 + y + -1y = -4xy + -4x2 + 1y + 4xy + 4x2 + -1y

Combine like terms: 4x2 + 4x2 = 8x2
4xy + 8x2 + y + -1y = -4xy + -4x2 + 1y + 4xy + 4x2 + -1y

Combine like terms: y + -1y = 0
4xy + 8x2 + 0 = -4xy + -4x2 + 1y + 4xy + 4x2 + -1y
4xy + 8x2 = -4xy + -4x2 + 1y + 4xy + 4x2 + -1y

Reorder the terms:
4xy + 8x2 = -4xy + 4xy + -4x2 + 4x2 + 1y + -1y

Combine like terms: -4xy + 4xy = 0
4xy + 8x2 = 0 + -4x2 + 4x2 + 1y + -1y
4xy + 8x2 = -4x2 + 4x2 + 1y + -1y

Combine like terms: -4x2 + 4x2 = 0
4xy + 8x2 = 0 + 1y + -1y
4xy + 8x2 = 1y + -1y

Combine like terms: 1y + -1y = 0
4xy + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(y + 2x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(y + 2x)' equal to zero and attempt to solve:

Simplifying
y + 2x = 0

Reorder the terms:
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
Solution
x = {0, -0.5y}

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