2x(5y+3)=9xy

Solution for 2x(5y+3)=9xy equation:

Simplifying
2x(5y + 3) = 9xy

Reorder the terms:
2x(3 + 5y) = 9xy
(3 * 2x + 5y * 2x) = 9xy
(6x + 10xy) = 9xy

Solving
6x + 10xy = 9xy

Solving for variable 'x'.

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

Add '-9xy' to each side of the equation.
6x + 10xy + -9xy = 9xy + -9xy

Combine like terms: 10xy + -9xy = 1xy
6x + 1xy = 9xy + -9xy

Combine like terms: 9xy + -9xy = 0
6x + 1xy = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + y) = 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 '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Add '-1y' to each side of the equation.
y + -1y = -6 + -1y

Combine like terms: y + -1y = 0
0 = -6 + -1y

Simplifying
0 = -6 + -1y

The solution to this equation could not be determined.

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