(5x^2y-2xy+9xy^2)-(8x^2+13xy+12xy^2)=

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Solution for (5x^2y-2xy+9xy^2)-(8x^2+13xy+12xy^2)= equation: 


Simplifying
(5x2y + -2xy + 9xy2) + -1(8x2 + 13xy + 12xy2) = 0

Reorder the terms:
(-2xy + 9xy2 + 5x2y) + -1(8x2 + 13xy + 12xy2) = 0

Remove parenthesis around (-2xy + 9xy2 + 5x2y)
-2xy + 9xy2 + 5x2y + -1(8x2 + 13xy + 12xy2) = 0

Reorder the terms:
-2xy + 9xy2 + 5x2y + -1(13xy + 12xy2 + 8x2) = 0
-2xy + 9xy2 + 5x2y + (13xy * -1 + 12xy2 * -1 + 8x2 * -1) = 0
-2xy + 9xy2 + 5x2y + (-13xy + -12xy2 + -8x2) = 0

Reorder the terms:
-2xy + -13xy + 9xy2 + -12xy2 + -8x2 + 5x2y = 0

Combine like terms: -2xy + -13xy = -15xy
-15xy + 9xy2 + -12xy2 + -8x2 + 5x2y = 0

Combine like terms: 9xy2 + -12xy2 = -3xy2
-15xy + -3xy2 + -8x2 + 5x2y = 0

Solving
-15xy + -3xy2 + -8x2 + 5x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15y + -3y2 + -8x + 5xy) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-15y + -3y2 + -8x + 5xy)' equal to zero and attempt to solve:

Simplifying
-15y + -3y2 + -8x + 5xy = 0

Reorder the terms:
-8x + 5xy + -15y + -3y2 = 0

Solving
-8x + 5xy + -15y + -3y2 = 0

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

Add '15y' to each side of the equation.
-8x + 5xy + -15y + 15y + -3y2 = 0 + 15y

Combine like terms: -15y + 15y = 0
-8x + 5xy + 0 + -3y2 = 0 + 15y
-8x + 5xy + -3y2 = 0 + 15y
Remove the zero:
-8x + 5xy + -3y2 = 15y

Add '3y2' to each side of the equation.
-8x + 5xy + -3y2 + 3y2 = 15y + 3y2

Combine like terms: -3y2 + 3y2 = 0
-8x + 5xy + 0 = 15y + 3y2
-8x + 5xy = 15y + 3y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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