6t^2+12t+6=0

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

Simplifying
6t2 + 12t + 6 = 0

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

Solving
6 + 12t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 2t + t2) = 0

Factor a trinomial.
6((1 + t)(1 + t)) = 0

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

Simplifying
1 + t = 0

Solving
1 + t = 0

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 + -1

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

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

Simplifying
t = -1
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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 + -1

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

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

Simplifying
t = -1
Solution
t = {-1, -1}