Y(x-5)=0

Solution for Y(x-5)=0 equation:

Simplifying
Y(x + -5) = 0

Reorder the terms:
Y(-5 + x) = 0
(-5 * Y + x * Y) = 0
(-5Y + xY) = 0

Solving
-5Y + xY = 0

Solving for variable 'Y'.

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

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

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

Simplifying
Y = 0

Solving
Y = 0

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

Simplifying
Y = 0
Subproblem 2
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

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

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

Combine like terms: 0 + 5 = 5
x = 5

Add '-1x' to each side of the equation.
x + -1x = 5 + -1x

Combine like terms: x + -1x = 0
0 = 5 + -1x

Simplifying
0 = 5 + -1x

The solution to this equation could not be determined.

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