(9x^2y-7xy+6xy^2)-(6x^2y+8xy+3xy^2)=

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Solution for (9x^2y-7xy+6xy^2)-(6x^2y+8xy+3xy^2)= equation: 


Simplifying
(9x2y + -7xy + 6xy2) + -1(6x2y + 8xy + 3xy2) = 0

Reorder the terms:
(-7xy + 6xy2 + 9x2y) + -1(6x2y + 8xy + 3xy2) = 0

Remove parenthesis around (-7xy + 6xy2 + 9x2y)
-7xy + 6xy2 + 9x2y + -1(6x2y + 8xy + 3xy2) = 0

Reorder the terms:
-7xy + 6xy2 + 9x2y + -1(8xy + 3xy2 + 6x2y) = 0
-7xy + 6xy2 + 9x2y + (8xy * -1 + 3xy2 * -1 + 6x2y * -1) = 0
-7xy + 6xy2 + 9x2y + (-8xy + -3xy2 + -6x2y) = 0

Reorder the terms:
-7xy + -8xy + 6xy2 + -3xy2 + 9x2y + -6x2y = 0

Combine like terms: -7xy + -8xy = -15xy
-15xy + 6xy2 + -3xy2 + 9x2y + -6x2y = 0

Combine like terms: 6xy2 + -3xy2 = 3xy2
-15xy + 3xy2 + 9x2y + -6x2y = 0

Combine like terms: 9x2y + -6x2y = 3x2y
-15xy + 3xy2 + 3x2y = 0

Solving
-15xy + 3xy2 + 3x2y = 0

Solving for variable 'x'.

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

Ignore the factor 3.

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 '(-5 + y + x)' equal to zero and attempt to solve:

Simplifying
-5 + y + x = 0

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

Solving
-5 + x + y = 0

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

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

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

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

Combine like terms: 0 + 5 = 5
x + y = 5

Add '-1y' to each side of the equation.
x + y + -1y = 5 + -1y

Combine like terms: y + -1y = 0
x + 0 = 5 + -1y
x = 5 + -1y

Simplifying
x = 5 + -1y
Solution
x = {5 + -1y}

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