2xy+2xy(2x+y-1)=0

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Solution for 2xy+2xy(2x+y-1)=0 equation: 


Simplifying
2xy + 2xy(2x + y + -1) = 0

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

Reorder the terms:
2xy + (-2xy + 2xy2 + 4x2y) = 0
2xy + (-2xy + 2xy2 + 4x2y) = 0

Combine like terms: 2xy + -2xy = 0
0 + 2xy2 + 4x2y = 0
2xy2 + 4x2y = 0

Solving
2xy2 + 4x2y = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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 = {-0.5y}

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