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

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

Simplifying
-3t2 + 6t + -1 = 0

Reorder the terms:
-1 + 6t + -3t2 = 0

Solving
-1 + 6t + -3t2 = 0

Solving for variable 't'.

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

Divide each side by '-3'.
0.3333333333 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -2t + -0.3333333333 + t2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -2t + t2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -2t + t2 = 0 + -0.3333333333
-2t + t2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-2t + t2 = -0.3333333333

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -0.3333333333 + 1

Reorder the terms:
1 + -2t + t2 = -0.3333333333 + 1

Combine like terms: -0.3333333333 + 1 = 0.6666666667
1 + -2t + t2 = 0.6666666667

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.6666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(t + -1) equal to 0.816496581 and -0.816496581.

Subproblem 1
t + -1 = 0.816496581

Simplifying
t + -1 = 0.816496581

Reorder the terms:
-1 + t = 0.816496581

Solving
-1 + t = 0.816496581

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.816496581 + 1
t = 0.816496581 + 1

Combine like terms: 0.816496581 + 1 = 1.816496581
t = 1.816496581

Simplifying
t = 1.816496581

Subproblem 2
t + -1 = -0.816496581

Simplifying
t + -1 = -0.816496581

Reorder the terms:
-1 + t = -0.816496581

Solving
-1 + t = -0.816496581

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.816496581 + 1
t = -0.816496581 + 1

Combine like terms: -0.816496581 + 1 = 0.183503419
t = 0.183503419

Simplifying
t = 0.183503419

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.816496581, 0.183503419}