81y^3-y=0

Solution for 81y^3-y=0 equation:

Simplifying
81y3 + -1y = 0

Reorder the terms:
-1y + 81y3 = 0

Solving
-1y + 81y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + 81y2) = 0

Factor a difference between two squares.
y((1 + 9y)(-1 + 9y)) = 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 + 9y)' equal to zero and attempt to solve:

Simplifying
1 + 9y = 0

Solving
1 + 9y = 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 + 9y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9y = 0 + -1
9y = 0 + -1

Combine like terms: 0 + -1 = -1
9y = -1

Divide each side by '9'.
y = -0.1111111111

Simplifying
y = -0.1111111111
Subproblem 3
Set the factor '(-1 + 9y)' equal to zero and attempt to solve:

Simplifying
-1 + 9y = 0

Solving
-1 + 9y = 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 + 9y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 9y = 0 + 1
9y = 0 + 1

Combine like terms: 0 + 1 = 1
9y = 1

Divide each side by '9'.
y = 0.1111111111

Simplifying
y = 0.1111111111
Solution
y = {0, -0.1111111111, 0.1111111111}