3xy+2xy(2x+y-1)=0

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Solution for 3xy+2xy(2x+y-1)=0 equation: 


Simplifying
3xy + 2xy(2x + y + -1) = 0

Reorder the terms:
3xy + 2xy(-1 + 2x + y) = 0
3xy + (-1 * 2xy + 2x * 2xy + y * 2xy) = 0

Reorder the terms:
3xy + (-2xy + 2xy2 + 4x2y) = 0
3xy + (-2xy + 2xy2 + 4x2y) = 0

Combine like terms: 3xy + -2xy = 1xy
1xy + 2xy2 + 4x2y = 0

Solving
1xy + 2xy2 + 4x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(1 + 2y + 4x) = 0


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 '(1 + 2y + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 2y + 4x = 0

Reorder the terms:
1 + 4x + 2y = 0

Solving
1 + 4x + 2y = 0

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

Add '-1' to each side of the equation.
1 + 4x + -1 + 2y = 0 + -1

Reorder the terms:
1 + -1 + 4x + 2y = 0 + -1

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

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

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

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

Divide each side by '4'.
x = -0.25 + -0.5y

Simplifying
x = -0.25 + -0.5y
Solution
x = {-0.25 + -0.5y}

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