6t^2+12t-4=0

Solution for 6t^2+12t-4=0 equation:

Simplifying
6t2 + 12t + -4 = 0

Reorder the terms:
-4 + 12t + 6t2 = 0

Solving
-4 + 12t + 6t2 = 0

Solving for variable 't'.

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

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

Simplifying
-2 + 6t + 3t2 = 0

Solving
-2 + 6t + 3t2 = 0

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 = 1.6666666667
1 + 2t + t2 = 1.6666666667

Factor a perfect square on the left side:
(t + 1)(t + 1) = 1.6666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(t + 1) equal to 1.290994449 and -1.290994449.

Subproblem 1
t + 1 = 1.290994449

Simplifying
t + 1 = 1.290994449

Reorder the terms:
1 + t = 1.290994449

Solving
1 + t = 1.290994449

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 = 1.290994449 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.290994449 + -1
t = 1.290994449 + -1

Combine like terms: 1.290994449 + -1 = 0.290994449
t = 0.290994449

Simplifying
t = 0.290994449

Subproblem 2
t + 1 = -1.290994449

Simplifying
t + 1 = -1.290994449

Reorder the terms:
1 + t = -1.290994449

Solving
1 + t = -1.290994449

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 = -1.290994449 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.290994449 + -1
t = -1.290994449 + -1

Combine like terms: -1.290994449 + -1 = -2.290994449
t = -2.290994449

Simplifying
t = -2.290994449

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.290994449, -2.290994449}
Solution
t = {0.290994449, -2.290994449}