(x^2y-3y^2+5xy^2)-(-x^2y+3xy^2-3y^2)=0

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Solution for (x^2y-3y^2+5xy^2)-(-x^2y+3xy^2-3y^2)=0 equation: 


Simplifying
(x2y + -3y2 + 5xy2) + -1(-1x2y + 3xy2 + -3y2) = 0

Reorder the terms:
(5xy2 + x2y + -3y2) + -1(-1x2y + 3xy2 + -3y2) = 0

Remove parenthesis around (5xy2 + x2y + -3y2)
5xy2 + x2y + -3y2 + -1(-1x2y + 3xy2 + -3y2) = 0

Reorder the terms:
5xy2 + x2y + -3y2 + -1(3xy2 + -1x2y + -3y2) = 0
5xy2 + x2y + -3y2 + (3xy2 * -1 + -1x2y * -1 + -3y2 * -1) = 0
5xy2 + x2y + -3y2 + (-3xy2 + 1x2y + 3y2) = 0

Reorder the terms:
5xy2 + -3xy2 + x2y + 1x2y + -3y2 + 3y2 = 0

Combine like terms: 5xy2 + -3xy2 = 2xy2
2xy2 + x2y + 1x2y + -3y2 + 3y2 = 0

Combine like terms: x2y + 1x2y = 2x2y
2xy2 + 2x2y + -3y2 + 3y2 = 0

Combine like terms: -3y2 + 3y2 = 0
2xy2 + 2x2y + 0 = 0
2xy2 + 2x2y = 0

Solving
2xy2 + 2x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2xy'.
2xy(y + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
y + x = 0

Reorder the terms:
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {-1y}

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