y=y(y-5)

Solution for y=y(y-5) equation:

Simplifying
y = y(y + -5)

Reorder the terms:
y = y(-5 + y)
y = (-5 * y + y * y)
y = (-5y + y2)

Solving
y = -5y + y2

Solving for variable 'y'.

Combine like terms: y + 5y = 6y
6y + -1y2 = -5y + y2 + 5y + -1y2

Reorder the terms:
6y + -1y2 = -5y + 5y + y2 + -1y2

Combine like terms: -5y + 5y = 0
6y + -1y2 = 0 + y2 + -1y2
6y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(6 + -1y) = 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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

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

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

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {0, 6}