2t^3-6t+5t=0

Solution for 2t^3-6t+5t=0 equation:

Simplifying
2t3 + -6t + 5t = 0

Reorder the terms:
-6t + 5t + 2t3 = 0

Combine like terms: -6t + 5t = -1t
-1t + 2t3 = 0

Solving
-1t + 2t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-1 + 2t2) = 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 + 2t2)' equal to zero and attempt to solve:

Simplifying
-1 + 2t2 = 0

Solving
-1 + 2t2 = 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 + 2t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2t2 = 0 + 1
2t2 = 0 + 1

Combine like terms: 0 + 1 = 1
2t2 = 1

Divide each side by '2'.
t2 = 0.5

Simplifying
t2 = 0.5

Take the square root of each side:
t = {-0.707106781, 0.707106781}
Solution
t = {0, -0.707106781, 0.707106781}