2t^2-12t+6=0

Solution for 2t^2-12t+6=0 equation:

Simplifying
2t2 + -12t + 6 = 0

Reorder the terms:
6 + -12t + 2t2 = 0

Solving
6 + -12t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -6t + t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -6t + t2)' equal to zero and attempt to solve:

Simplifying
3 + -6t + t2 = 0

Solving
3 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -6t + -3 + t2 = 0 + -3

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

Combine like terms: 3 + -3 = 0
0 + -6t + t2 = 0 + -3
-6t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-6t + t2 = -3

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = -3 + 9

Reorder the terms:
9 + -6t + t2 = -3 + 9

Combine like terms: -3 + 9 = 6
9 + -6t + t2 = 6

Factor a perfect square on the left side:
(t + -3)(t + -3) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(t + -3) equal to 2.449489743 and -2.449489743.

Subproblem 1
t + -3 = 2.449489743

Simplifying
t + -3 = 2.449489743

Reorder the terms:
-3 + t = 2.449489743

Solving
-3 + t = 2.449489743

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 2.449489743 + 3

Combine like terms: -3 + 3 = 0
0 + t = 2.449489743 + 3
t = 2.449489743 + 3

Combine like terms: 2.449489743 + 3 = 5.449489743
t = 5.449489743

Simplifying
t = 5.449489743

Subproblem 2
t + -3 = -2.449489743

Simplifying
t + -3 = -2.449489743

Reorder the terms:
-3 + t = -2.449489743

Solving
-3 + t = -2.449489743

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -2.449489743 + 3

Combine like terms: -3 + 3 = 0
0 + t = -2.449489743 + 3
t = -2.449489743 + 3

Combine like terms: -2.449489743 + 3 = 0.550510257
t = 0.550510257

Simplifying
t = 0.550510257

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.449489743, 0.550510257}
Solution
t = {5.449489743, 0.550510257}