24t^3-3t=0

Solution for 24t^3-3t=0 equation:

Simplifying
24t3 + -3t = 0

Reorder the terms:
-3t + 24t3 = 0

Solving
-3t + 24t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3t'.
3t(-1 + 8t2) = 0

Ignore the factor 3.
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 + 8t2)' equal to zero and attempt to solve:

Simplifying
-1 + 8t2 = 0

Solving
-1 + 8t2 = 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 + 8t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8t2 = 0 + 1
8t2 = 0 + 1

Combine like terms: 0 + 1 = 1
8t2 = 1

Divide each side by '8'.
t2 = 0.125

Simplifying
t2 = 0.125

Take the square root of each side:
t = {-0.353553391, 0.353553391}
Solution
t = {0, -0.353553391, 0.353553391}