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

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

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

Reorder the terms:
0 = 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)

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

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

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

Solving
0 = -3x + 3xy

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
0 + 3x = -3x + 3x + 3xy
Remove the zero:
3x = -3x + 3x + 3xy

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

Add '-3xy' to each side of the equation.
3x + -3xy = 3xy + -3xy

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

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + -1y) = 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 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 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 + -1y = 0 + -1

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

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

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

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

Simplifying
0 = -1 + y

The solution to this equation could not be determined.

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