(3t+2)(t+6)=0

Solution for (3t+2)(t+6)=0 equation:

Simplifying
(3t + 2)(t + 6) = 0

Reorder the terms:
(2 + 3t)(t + 6) = 0

Reorder the terms:
(2 + 3t)(6 + t) = 0

Multiply (2 + 3t) * (6 + t)
(2(6 + t) + 3t * (6 + t)) = 0
((6 * 2 + t * 2) + 3t * (6 + t)) = 0
((12 + 2t) + 3t * (6 + t)) = 0
(12 + 2t + (6 * 3t + t * 3t)) = 0
(12 + 2t + (18t + 3t2)) = 0

Combine like terms: 2t + 18t = 20t
(12 + 20t + 3t2) = 0

Solving
12 + 20t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(6 + t)(2 + 3t) = 0

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

Simplifying
6 + t = 0

Solving
6 + t = 0

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

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

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

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

Simplifying
t = -6
Subproblem 2
Set the factor '(2 + 3t)' equal to zero and attempt to solve:

Simplifying
2 + 3t = 0

Solving
2 + 3t = 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 + 3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3t = 0 + -2
3t = 0 + -2

Combine like terms: 0 + -2 = -2
3t = -2

Divide each side by '3'.
t = -0.6666666667

Simplifying
t = -0.6666666667
Solution
t = {-6, -0.6666666667}