8t^2+12t+4=0

Solution for 8t^2+12t+4=0 equation:

Simplifying
8t2 + 12t + 4 = 0

Reorder the terms:
4 + 12t + 8t2 = 0

Solving
4 + 12t + 8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 3t + 2t2) = 0

Factor a trinomial.
4((1 + t)(1 + 2t)) = 0

Ignore the factor 4.
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 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {-1, -0.5}