t^5-81t=0

Solution for t^5-81t=0 equation:

Simplifying
t5 + -81t = 0

Reorder the terms:
-81t + t5 = 0

Solving
-81t + t5 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-81 + t4) = 0

Factor a difference between two squares.
t((9 + t2)(-9 + t2)) = 0

Factor a difference between two squares.
t((9 + t2)((3 + t)(-3 + t))) = 0

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 '(9 + t2)' equal to zero and attempt to solve:

Simplifying
9 + t2 = 0

Solving
9 + t2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + t2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + t2 = 0 + -9
t2 = 0 + -9

Combine like terms: 0 + -9 = -9
t2 = -9

Simplifying
t2 = -9

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

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

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

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

Simplifying
t = -3
Subproblem 4
Set the factor '(-3 + t)' equal to zero and attempt to solve:

Simplifying
-3 + t = 0

Solving
-3 + t = 0

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

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

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

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

Simplifying
t = 3
Solution
t = {0, -3, 3}