(3x^2y-3xy+6xy^2)-(2x^2y+4xy+5xy^2)=

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Solution for (3x^2y-3xy+6xy^2)-(2x^2y+4xy+5xy^2)= equation: 


Simplifying
(3x2y + -3xy + 6xy2) + -1(2x2y + 4xy + 5xy2) = 0

Reorder the terms:
(-3xy + 6xy2 + 3x2y) + -1(2x2y + 4xy + 5xy2) = 0

Remove parenthesis around (-3xy + 6xy2 + 3x2y)
-3xy + 6xy2 + 3x2y + -1(2x2y + 4xy + 5xy2) = 0

Reorder the terms:
-3xy + 6xy2 + 3x2y + -1(4xy + 5xy2 + 2x2y) = 0
-3xy + 6xy2 + 3x2y + (4xy * -1 + 5xy2 * -1 + 2x2y * -1) = 0
-3xy + 6xy2 + 3x2y + (-4xy + -5xy2 + -2x2y) = 0

Reorder the terms:
-3xy + -4xy + 6xy2 + -5xy2 + 3x2y + -2x2y = 0

Combine like terms: -3xy + -4xy = -7xy
-7xy + 6xy2 + -5xy2 + 3x2y + -2x2y = 0

Combine like terms: 6xy2 + -5xy2 = 1xy2
-7xy + 1xy2 + 3x2y + -2x2y = 0

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

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

Solving for variable 'x'.

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

Simplifying
-7 + y + x = 0

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

Solving
-7 + x + y = 0

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

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

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

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

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

Add '-1y' to each side of the equation.
x + y + -1y = 7 + -1y

Combine like terms: y + -1y = 0
x + 0 = 7 + -1y
x = 7 + -1y

Simplifying
x = 7 + -1y
Solution
x = {7 + -1y}

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