(3x^2y-4xy)-(5x^2y-7xy^2)=0

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Solution for (3x^2y-4xy)-(5x^2y-7xy^2)=0 equation: 


Simplifying
(3x2y + -4xy) + -1(5x2y + -7xy2) = 0

Reorder the terms:
(-4xy + 3x2y) + -1(5x2y + -7xy2) = 0

Remove parenthesis around (-4xy + 3x2y)
-4xy + 3x2y + -1(5x2y + -7xy2) = 0

Reorder the terms:
-4xy + 3x2y + -1(-7xy2 + 5x2y) = 0
-4xy + 3x2y + (-7xy2 * -1 + 5x2y * -1) = 0
-4xy + 3x2y + (7xy2 + -5x2y) = 0

Reorder the terms:
-4xy + 7xy2 + 3x2y + -5x2y = 0

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

Solving
-4xy + 7xy2 + -2x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(-4 + 7y + -2x) = 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 '(-4 + 7y + -2x)' equal to zero and attempt to solve:

Simplifying
-4 + 7y + -2x = 0

Reorder the terms:
-4 + -2x + 7y = 0

Solving
-4 + -2x + 7y = 0

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

Add '4' to each side of the equation.
-4 + -2x + 4 + 7y = 0 + 4

Reorder the terms:
-4 + 4 + -2x + 7y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2x + 7y = 0 + 4
-2x + 7y = 0 + 4

Combine like terms: 0 + 4 = 4
-2x + 7y = 4

Add '-7y' to each side of the equation.
-2x + 7y + -7y = 4 + -7y

Combine like terms: 7y + -7y = 0
-2x + 0 = 4 + -7y
-2x = 4 + -7y

Divide each side by '-2'.
x = -2 + 3.5y

Simplifying
x = -2 + 3.5y
Solution
x = {-2 + 3.5y}

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