(6x^2y-7xy+9xy^2)-(5x^2y+8xy+2xy^2)=

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Solution for (6x^2y-7xy+9xy^2)-(5x^2y+8xy+2xy^2)= equation: 


Simplifying
(6x2y + -7xy + 9xy2) + -1(5x2y + 8xy + 2xy2) = 0

Reorder the terms:
(-7xy + 9xy2 + 6x2y) + -1(5x2y + 8xy + 2xy2) = 0

Remove parenthesis around (-7xy + 9xy2 + 6x2y)
-7xy + 9xy2 + 6x2y + -1(5x2y + 8xy + 2xy2) = 0

Reorder the terms:
-7xy + 9xy2 + 6x2y + -1(8xy + 2xy2 + 5x2y) = 0
-7xy + 9xy2 + 6x2y + (8xy * -1 + 2xy2 * -1 + 5x2y * -1) = 0
-7xy + 9xy2 + 6x2y + (-8xy + -2xy2 + -5x2y) = 0

Reorder the terms:
-7xy + -8xy + 9xy2 + -2xy2 + 6x2y + -5x2y = 0

Combine like terms: -7xy + -8xy = -15xy
-15xy + 9xy2 + -2xy2 + 6x2y + -5x2y = 0

Combine like terms: 9xy2 + -2xy2 = 7xy2
-15xy + 7xy2 + 6x2y + -5x2y = 0

Combine like terms: 6x2y + -5x2y = 1x2y
-15xy + 7xy2 + 1x2y = 0

Solving
-15xy + 7xy2 + 1x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-15 + 7y + 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 '(-15 + 7y + x)' equal to zero and attempt to solve:

Simplifying
-15 + 7y + x = 0

Reorder the terms:
-15 + x + 7y = 0

Solving
-15 + x + 7y = 0

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

Add '15' to each side of the equation.
-15 + x + 15 + 7y = 0 + 15

Reorder the terms:
-15 + 15 + x + 7y = 0 + 15

Combine like terms: -15 + 15 = 0
0 + x + 7y = 0 + 15
x + 7y = 0 + 15

Combine like terms: 0 + 15 = 15
x + 7y = 15

Add '-7y' to each side of the equation.
x + 7y + -7y = 15 + -7y

Combine like terms: 7y + -7y = 0
x + 0 = 15 + -7y
x = 15 + -7y

Simplifying
x = 15 + -7y
Solution
x = {15 + -7y}

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