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

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


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

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

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

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

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

Combine like terms: -3xy + -5xy = -8xy
-8xy + 5xy2 + -4xy2 + 6x2y + -3x2y = 0

Combine like terms: 5xy2 + -4xy2 = 1xy2
-8xy + 1xy2 + 6x2y + -3x2y = 0

Combine like terms: 6x2y + -3x2y = 3x2y
-8xy + 1xy2 + 3x2y = 0

Solving
-8xy + 1xy2 + 3x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-8 + y + 3x) = 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 '(-8 + y + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + y + 3x = 0

Reorder the terms:
-8 + 3x + y = 0

Solving
-8 + 3x + y = 0

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

Add '8' to each side of the equation.
-8 + 3x + 8 + y = 0 + 8

Reorder the terms:
-8 + 8 + 3x + y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x + y = 0 + 8
3x + y = 0 + 8

Combine like terms: 0 + 8 = 8
3x + y = 8

Add '-1y' to each side of the equation.
3x + y + -1y = 8 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 8 + -1y
3x = 8 + -1y

Divide each side by '3'.
x = 2.666666667 + -0.3333333333y

Simplifying
x = 2.666666667 + -0.3333333333y
Solution
x = {2.666666667 + -0.3333333333y}

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