3t^2+6t+2=0

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

Simplifying
3t2 + 6t + 2 = 0

Reorder the terms:
2 + 6t + 3t2 = 0

Solving
2 + 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'.
0.6666666667 + 2t + t2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 2t + -0.6666666667 + t2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 2t + t2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 2t + t2 = 0 + -0.6666666667
2t + t2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
2t + t2 = -0.6666666667

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 = -0.6666666667 + 1

Reorder the terms:
1 + 2t + t2 = -0.6666666667 + 1

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

Factor a perfect square on the left side:
(t + 1)(t + 1) = 0.3333333333

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(t + 1) equal to 0.577350269 and -0.577350269.

Subproblem 1
t + 1 = 0.577350269

Simplifying
t + 1 = 0.577350269

Reorder the terms:
1 + t = 0.577350269

Solving
1 + t = 0.577350269

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 = 0.577350269 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0.577350269 + -1
t = 0.577350269 + -1

Combine like terms: 0.577350269 + -1 = -0.422649731
t = -0.422649731

Simplifying
t = -0.422649731

Subproblem 2
t + 1 = -0.577350269

Simplifying
t + 1 = -0.577350269

Reorder the terms:
1 + t = -0.577350269

Solving
1 + t = -0.577350269

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 = -0.577350269 + -1

Combine like terms: 1 + -1 = 0
0 + t = -0.577350269 + -1
t = -0.577350269 + -1

Combine like terms: -0.577350269 + -1 = -1.577350269
t = -1.577350269

Simplifying
t = -1.577350269

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.422649731, -1.577350269}