0=t^3-t

Solution for 0=t^3-t equation:

Simplifying
0 = t3 + -1t

Reorder the terms:
0 = -1t + t3

Solving
0 = -1t + t3

Solving for variable 't'.
Remove the zero:
t + -1t3 = -1t + t3 + t + -1t3

Reorder the terms:
t + -1t3 = -1t + t + t3 + -1t3

Combine like terms: -1t + t = 0
t + -1t3 = 0 + t3 + -1t3
t + -1t3 = t3 + -1t3

Combine like terms: t3 + -1t3 = 0
t + -1t3 = 0

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

Factor a difference between two squares.
t((1 + t)(1 + -1t)) = 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 '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 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 + t = 0 + -1

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

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

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 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 + -1t = 0 + -1

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

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

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Solution
t = {0, -1, 1}