x(4y-9)+x(6-y)=0

Solution for x(4y-9)+x(6-y)=0 equation:

Simplifying
x(4y + -9) + x(6 + -1y) = 0

Reorder the terms:
x(-9 + 4y) + x(6 + -1y) = 0
(-9 * x + 4y * x) + x(6 + -1y) = 0
(-9x + 4xy) + x(6 + -1y) = 0
-9x + 4xy + (6 * x + -1y * x) = 0
-9x + 4xy + (6x + -1xy) = 0

Reorder the terms:
-9x + 6x + 4xy + -1xy = 0

Combine like terms: -9x + 6x = -3x
-3x + 4xy + -1xy = 0

Combine like terms: 4xy + -1xy = 3xy
-3x + 3xy = 0

Solving
-3x + 3xy = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-1 + y) = 0

Ignore the factor 3.
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 '(-1 + y)' equal to zero and attempt to solve:

Simplifying
-1 + y = 0

Solving
-1 + y = 0

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

Add '1' to each side of the equation.
-1 + 1 + y = 0 + 1

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

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

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

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

Simplifying
0 = 1 + -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}