(5x^2y+6xy)-(3x^2y+3xy^2)-(4xy-6xy^2)=

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Solution for (5x^2y+6xy)-(3x^2y+3xy^2)-(4xy-6xy^2)= equation: 


Simplifying
(5x2y + 6xy) + -1(3x2y + 3xy2) + -1(4xy + -6xy2) = 0

Reorder the terms:
(6xy + 5x2y) + -1(3x2y + 3xy2) + -1(4xy + -6xy2) = 0

Remove parenthesis around (6xy + 5x2y)
6xy + 5x2y + -1(3x2y + 3xy2) + -1(4xy + -6xy2) = 0

Reorder the terms:
6xy + 5x2y + -1(3xy2 + 3x2y) + -1(4xy + -6xy2) = 0
6xy + 5x2y + (3xy2 * -1 + 3x2y * -1) + -1(4xy + -6xy2) = 0
6xy + 5x2y + (-3xy2 + -3x2y) + -1(4xy + -6xy2) = 0
6xy + 5x2y + -3xy2 + -3x2y + (4xy * -1 + -6xy2 * -1) = 0
6xy + 5x2y + -3xy2 + -3x2y + (-4xy + 6xy2) = 0

Reorder the terms:
6xy + -4xy + -3xy2 + 6xy2 + 5x2y + -3x2y = 0

Combine like terms: 6xy + -4xy = 2xy
2xy + -3xy2 + 6xy2 + 5x2y + -3x2y = 0

Combine like terms: -3xy2 + 6xy2 = 3xy2
2xy + 3xy2 + 5x2y + -3x2y = 0

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

Solving
2xy + 3xy2 + 2x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(2 + 3y + 2x) = 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 '(2 + 3y + 2x)' equal to zero and attempt to solve:

Simplifying
2 + 3y + 2x = 0

Reorder the terms:
2 + 2x + 3y = 0

Solving
2 + 2x + 3y = 0

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

Add '-2' to each side of the equation.
2 + 2x + -2 + 3y = 0 + -2

Reorder the terms:
2 + -2 + 2x + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2x + 3y = 0 + -2
2x + 3y = 0 + -2

Combine like terms: 0 + -2 = -2
2x + 3y = -2

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

Combine like terms: 3y + -3y = 0
2x + 0 = -2 + -3y
2x = -2 + -3y

Divide each side by '2'.
x = -1 + -1.5y

Simplifying
x = -1 + -1.5y
Solution
x = {-1 + -1.5y}

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