3x+5xy=3xy+2x

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Solution for 3x+5xy=3xy+2x equation: 


Simplifying
3x + 5xy = 3xy + 2x

Reorder the terms:
3x + 5xy = 2x + 3xy

Solving
3x + 5xy = 2x + 3xy

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
3x + -2x + 5xy = 2x + -2x + 3xy

Combine like terms: 3x + -2x = 1x
1x + 5xy = 2x + -2x + 3xy

Combine like terms: 2x + -2x = 0
1x + 5xy = 0 + 3xy
1x + 5xy = 3xy

Add '-3xy' to each side of the equation.
1x + 5xy + -3xy = 3xy + -3xy

Combine like terms: 5xy + -3xy = 2xy
1x + 2xy = 3xy + -3xy

Combine like terms: 3xy + -3xy = 0
1x + 2xy = 0

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


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

Simplifying
1 + 2y = 0

Solving
1 + 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 + -1 + 2y = 0 + -1

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

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

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

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

Simplifying
0 = -1 + -2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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