y(5y-1)=0

Solution for y(5y-1)=0 equation:

Simplifying
y(5y + -1) = 0

Reorder the terms:
y(-1 + 5y) = 0
(-1 * y + 5y * y) = 0
(-1y + 5y2) = 0

Solving
-1y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + 5y) = 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 '(-1 + 5y)' equal to zero and attempt to solve:

Simplifying
-1 + 5y = 0

Solving
-1 + 5y = 0

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

Add '1' to each side of the equation.
-1 + 1 + 5y = 0 + 1

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

Combine like terms: 0 + 1 = 1
5y = 1

Divide each side by '5'.
y = 0.2

Simplifying
y = 0.2
Solution
y = {0, 0.2}