(3x^2y-5xy+12xy^2)-(5xy^2+4xy)=

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Solution for (3x^2y-5xy+12xy^2)-(5xy^2+4xy)= equation: 


Simplifying
(3x2y + -5xy + 12xy2) + -1(5xy2 + 4xy) = 0

Reorder the terms:
(-5xy + 12xy2 + 3x2y) + -1(5xy2 + 4xy) = 0

Remove parenthesis around (-5xy + 12xy2 + 3x2y)
-5xy + 12xy2 + 3x2y + -1(5xy2 + 4xy) = 0

Reorder the terms:
-5xy + 12xy2 + 3x2y + -1(4xy + 5xy2) = 0
-5xy + 12xy2 + 3x2y + (4xy * -1 + 5xy2 * -1) = 0
-5xy + 12xy2 + 3x2y + (-4xy + -5xy2) = 0

Reorder the terms:
-5xy + -4xy + 12xy2 + -5xy2 + 3x2y = 0

Combine like terms: -5xy + -4xy = -9xy
-9xy + 12xy2 + -5xy2 + 3x2y = 0

Combine like terms: 12xy2 + -5xy2 = 7xy2
-9xy + 7xy2 + 3x2y = 0

Solving
-9xy + 7xy2 + 3x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-9 + 7y + 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 '(-9 + 7y + 3x)' equal to zero and attempt to solve:

Simplifying
-9 + 7y + 3x = 0

Reorder the terms:
-9 + 3x + 7y = 0

Solving
-9 + 3x + 7y = 0

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

Add '9' to each side of the equation.
-9 + 3x + 9 + 7y = 0 + 9

Reorder the terms:
-9 + 9 + 3x + 7y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 3x + 7y = 0 + 9
3x + 7y = 0 + 9

Combine like terms: 0 + 9 = 9
3x + 7y = 9

Add '-7y' to each side of the equation.
3x + 7y + -7y = 9 + -7y

Combine like terms: 7y + -7y = 0
3x + 0 = 9 + -7y
3x = 9 + -7y

Divide each side by '3'.
x = 3 + -2.333333333y

Simplifying
x = 3 + -2.333333333y
Solution
x = {3 + -2.333333333y}

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