t^3-5t=0

Solution for t^3-5t=0 equation:

Simplifying
t3 + -5t = 0

Reorder the terms:
-5t + t3 = 0

Solving
-5t + t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-5 + t2) = 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 '(-5 + t2)' equal to zero and attempt to solve:

Simplifying
-5 + t2 = 0

Solving
-5 + t2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + t2 = 0 + 5
t2 = 0 + 5

Combine like terms: 0 + 5 = 5
t2 = 5

Simplifying
t2 = 5

Take the square root of each side:
t = {-2.236067978, 2.236067978}
Solution
t = {0, -2.236067978, 2.236067978}