9x[4+y]=5x[y+12]

Solution for 9x[4+y]=5x[y+12] equation:

Simplifying
9x[4 + y] = 5x[y + 12]
[4 * 9x + y * 9x] = 5x[y + 12]
[36x + 9xy] = 5x[y + 12]

Reorder the terms:
36x + 9xy = 5x[12 + y]
36x + 9xy = [12 * 5x + y * 5x]
36x + 9xy = [60x + 5xy]

Solving
36x + 9xy = 60x + 5xy

Solving for variable 'x'.

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

Add '-60x' to each side of the equation.
36x + -60x + 9xy = 60x + -60x + 5xy

Combine like terms: 36x + -60x = -24x
-24x + 9xy = 60x + -60x + 5xy

Combine like terms: 60x + -60x = 0
-24x + 9xy = 0 + 5xy
-24x + 9xy = 5xy

Add '-5xy' to each side of the equation.
-24x + 9xy + -5xy = 5xy + -5xy

Combine like terms: 9xy + -5xy = 4xy
-24x + 4xy = 5xy + -5xy

Combine like terms: 5xy + -5xy = 0
-24x + 4xy = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-6 + y) = 0

Ignore the factor 4.
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}