(8t+4)(3t+6)=0

Solution for (8t+4)(3t+6)=0 equation:

Simplifying
(8t + 4)(3t + 6) = 0

Reorder the terms:
(4 + 8t)(3t + 6) = 0

Reorder the terms:
(4 + 8t)(6 + 3t) = 0

Multiply (4 + 8t) * (6 + 3t)
(4(6 + 3t) + 8t * (6 + 3t)) = 0
((6 * 4 + 3t * 4) + 8t * (6 + 3t)) = 0
((24 + 12t) + 8t * (6 + 3t)) = 0
(24 + 12t + (6 * 8t + 3t * 8t)) = 0
(24 + 12t + (48t + 24t2)) = 0

Combine like terms: 12t + 48t = 60t
(24 + 60t + 24t2) = 0

Solving
24 + 60t + 24t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '12'.
12(2 + 5t + 2t2) = 0

Factor a trinomial.
12((2 + t)(1 + 2t)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 0

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

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

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

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

Simplifying
t = -2
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 = {-2, -0.5}