(8x^2y-4xy+3xy^2)-(7x^2y+2xy+2xy^2)=0

Solution for (8x^2y-4xy+3xy^2)-(7x^2y+2xy+2xy^2)=0 equation:

Simplifying
(8x2y + -4xy + 3xy2) + -1(7x2y + 2xy + 2xy2) = 0

Reorder the terms:
(-4xy + 3xy2 + 8x2y) + -1(7x2y + 2xy + 2xy2) = 0

Remove parenthesis around (-4xy + 3xy2 + 8x2y)
-4xy + 3xy2 + 8x2y + -1(7x2y + 2xy + 2xy2) = 0

Reorder the terms:
-4xy + 3xy2 + 8x2y + -1(2xy + 2xy2 + 7x2y) = 0
-4xy + 3xy2 + 8x2y + (2xy * -1 + 2xy2 * -1 + 7x2y * -1) = 0
-4xy + 3xy2 + 8x2y + (-2xy + -2xy2 + -7x2y) = 0

Reorder the terms:
-4xy + -2xy + 3xy2 + -2xy2 + 8x2y + -7x2y = 0

Combine like terms: -4xy + -2xy = -6xy
-6xy + 3xy2 + -2xy2 + 8x2y + -7x2y = 0

Combine like terms: 3xy2 + -2xy2 = 1xy2
-6xy + 1xy2 + 8x2y + -7x2y = 0

Combine like terms: 8x2y + -7x2y = 1x2y
-6xy + 1xy2 + 1x2y = 0

Solving
-6xy + 1xy2 + 1x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-6 + y + x) = 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 '(-6 + y + x)' equal to zero and attempt to solve:

Simplifying
-6 + y + x = 0

Reorder the terms:
-6 + x + y = 0

Solving
-6 + x + y = 0

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

Add '6' to each side of the equation.
-6 + x + 6 + y = 0 + 6

Reorder the terms:
-6 + 6 + x + y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x + y = 0 + 6
x + y = 0 + 6

Combine like terms: 0 + 6 = 6
x + y = 6

Add '-1y' to each side of the equation.
x + y + -1y = 6 + -1y

Combine like terms: y + -1y = 0
x + 0 = 6 + -1y
x = 6 + -1y

Simplifying
x = 6 + -1y
Solution
x = {6 + -1y}