2x(2y-3)=3x(3y-5)

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Solution for 2x(2y-3)=3x(3y-5) equation: 


Simplifying
2x(2y + -3) = 3x(3y + -5)

Reorder the terms:
2x(-3 + 2y) = 3x(3y + -5)
(-3 * 2x + 2y * 2x) = 3x(3y + -5)
(-6x + 4xy) = 3x(3y + -5)

Reorder the terms:
-6x + 4xy = 3x(-5 + 3y)
-6x + 4xy = (-5 * 3x + 3y * 3x)
-6x + 4xy = (-15x + 9xy)

Solving
-6x + 4xy = -15x + 9xy

Solving for variable 'x'.

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

Add '15x' to each side of the equation.
-6x + 15x + 4xy = -15x + 15x + 9xy

Combine like terms: -6x + 15x = 9x
9x + 4xy = -15x + 15x + 9xy

Combine like terms: -15x + 15x = 0
9x + 4xy = 0 + 9xy
9x + 4xy = 9xy

Add '-9xy' to each side of the equation.
9x + 4xy + -9xy = 9xy + -9xy

Combine like terms: 4xy + -9xy = -5xy
9x + -5xy = 9xy + -9xy

Combine like terms: 9xy + -9xy = 0
9x + -5xy = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + -5y) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(9 + -5y)' equal to zero and attempt to solve:

Simplifying
9 + -5y = 0

Solving
9 + -5y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5y = 0 + -9
-5y = 0 + -9

Combine like terms: 0 + -9 = -9
-5y = -9

Add '5y' to each side of the equation.
-5y + 5y = -9 + 5y

Combine like terms: -5y + 5y = 0
0 = -9 + 5y

Simplifying
0 = -9 + 5y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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