-3t(2t^2-6t+1)=0

Solution for -3t(2t^2-6t+1)=0 equation:

Simplifying
-3t(2t2 + -6t + 1) = 0

Reorder the terms:
-3t(1 + -6t + 2t2) = 0
(1 * -3t + -6t * -3t + 2t2 * -3t) = 0
(-3t + 18t2 + -6t3) = 0

Solving
-3t + 18t2 + -6t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3t'.
3t(-1 + 6t + -2t2) = 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 + 6t + -2t2)' equal to zero and attempt to solve:

Simplifying
-1 + 6t + -2t2 = 0

Solving
-1 + 6t + -2t2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.5 + -3t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -3t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -3t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -3t + t2 = 0 + -0.5
-3t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-3t + t2 = -0.5

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -0.5 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -0.5 + 2.25

Combine like terms: -0.5 + 2.25 = 1.75
2.25 + -3t + t2 = 1.75

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
t + -1.5 = 1.322875656

Simplifying
t + -1.5 = 1.322875656

Reorder the terms:
-1.5 + t = 1.322875656

Solving
-1.5 + t = 1.322875656

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 1.322875656 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.322875656 + 1.5
t = 1.322875656 + 1.5

Combine like terms: 1.322875656 + 1.5 = 2.822875656
t = 2.822875656

Simplifying
t = 2.822875656

Subproblem 2
t + -1.5 = -1.322875656

Simplifying
t + -1.5 = -1.322875656

Reorder the terms:
-1.5 + t = -1.322875656

Solving
-1.5 + t = -1.322875656

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -1.322875656 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.322875656 + 1.5
t = -1.322875656 + 1.5

Combine like terms: -1.322875656 + 1.5 = 0.177124344
t = 0.177124344

Simplifying
t = 0.177124344

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.822875656, 0.177124344}
Solution
t = {0, 2.822875656, 0.177124344}