=(8x^2y-3xy+7xy^2)-(5x^2y+3xy+2xy^2)

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Solution for =(8x^2y-3xy+7xy^2)-(5x^2y+3xy+2xy^2) equation: 


Simplifying
0 = (8x2y + -3xy + 7xy2) + -1(5x2y + 3xy + 2xy2)

Reorder the terms:
0 = (-3xy + 7xy2 + 8x2y) + -1(5x2y + 3xy + 2xy2)

Remove parenthesis around (-3xy + 7xy2 + 8x2y)
0 = -3xy + 7xy2 + 8x2y + -1(5x2y + 3xy + 2xy2)

Reorder the terms:
0 = -3xy + 7xy2 + 8x2y + -1(3xy + 2xy2 + 5x2y)
0 = -3xy + 7xy2 + 8x2y + (3xy * -1 + 2xy2 * -1 + 5x2y * -1)
0 = -3xy + 7xy2 + 8x2y + (-3xy + -2xy2 + -5x2y)

Reorder the terms:
0 = -3xy + -3xy + 7xy2 + -2xy2 + 8x2y + -5x2y

Combine like terms: -3xy + -3xy = -6xy
0 = -6xy + 7xy2 + -2xy2 + 8x2y + -5x2y

Combine like terms: 7xy2 + -2xy2 = 5xy2
0 = -6xy + 5xy2 + 8x2y + -5x2y

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

Solving
0 = -6xy + 5xy2 + 3x2y

Solving for variable 'x'.
Remove the zero:
6xy + -5xy2 + -3x2y = -6xy + 5xy2 + 3x2y + 6xy + -5xy2 + -3x2y

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(6 + -5y + -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 '(6 + -5y + -3x)' equal to zero and attempt to solve:

Simplifying
6 + -5y + -3x = 0

Reorder the terms:
6 + -3x + -5y = 0

Solving
6 + -3x + -5y = 0

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

Add '-6' to each side of the equation.
6 + -3x + -6 + -5y = 0 + -6

Reorder the terms:
6 + -6 + -3x + -5y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -3x + -5y = 0 + -6
-3x + -5y = 0 + -6

Combine like terms: 0 + -6 = -6
-3x + -5y = -6

Add '5y' to each side of the equation.
-3x + -5y + 5y = -6 + 5y

Combine like terms: -5y + 5y = 0
-3x + 0 = -6 + 5y
-3x = -6 + 5y

Divide each side by '-3'.
x = 2 + -1.666666667y

Simplifying
x = 2 + -1.666666667y
Solution
x = {2 + -1.666666667y}

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