81t^3-9t=0

Solution for 81t^3-9t=0 equation:

Simplifying
81t3 + -9t = 0

Reorder the terms:
-9t + 81t3 = 0

Solving
-9t + 81t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '9t'.
9t(-1 + 9t2) = 0

Factor a difference between two squares.
9t((1 + 3t)(-1 + 3t)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(1 + 3t)' equal to zero and attempt to solve:

Simplifying
1 + 3t = 0

Solving
1 + 3t = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3t = 0 + -1
3t = 0 + -1

Combine like terms: 0 + -1 = -1
3t = -1

Divide each side by '3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Subproblem 3
Set the factor '(-1 + 3t)' equal to zero and attempt to solve:

Simplifying
-1 + 3t = 0

Solving
-1 + 3t = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3t = 0 + 1
3t = 0 + 1

Combine like terms: 0 + 1 = 1
3t = 1

Divide each side by '3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Solution
t = {0, -0.3333333333, 0.3333333333}