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

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

Simplifying
3t3 + -3t2 + t = 0

Reorder the terms:
t + -3t2 + 3t3 = 0

Solving
t + -3t2 + 3t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(1 + -3t + 3t2) = 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 + -3t + 3t2)' equal to zero and attempt to solve:

Simplifying
1 + -3t + 3t2 = 0

Solving
1 + -3t + 3t2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
0.3333333333 + -1t + t2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1t + -0.3333333333 + t2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1t + t2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1t + t2 = 0 + -0.3333333333
-1t + t2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1t + t2 = -0.3333333333

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = -0.3333333333 + 0.25

Reorder the terms:
0.25 + -1t + t2 = -0.3333333333 + 0.25

Combine like terms: -0.3333333333 + 0.25 = -0.0833333333
0.25 + -1t + t2 = -0.0833333333

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = -0.0833333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {0}