(3t+7)(t+6)=0

Solution for (3t+7)(t+6)=0 equation:

Simplifying
(3t + 7)(t + 6) = 0

Reorder the terms:
(7 + 3t)(t + 6) = 0

Reorder the terms:
(7 + 3t)(6 + t) = 0

Multiply (7 + 3t) * (6 + t)
(7(6 + t) + 3t * (6 + t)) = 0
((6 * 7 + t * 7) + 3t * (6 + t)) = 0
((42 + 7t) + 3t * (6 + t)) = 0
(42 + 7t + (6 * 3t + t * 3t)) = 0
(42 + 7t + (18t + 3t2)) = 0

Combine like terms: 7t + 18t = 25t
(42 + 25t + 3t2) = 0

Solving
42 + 25t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(6 + t)(7 + 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 '(7 + 3t)' equal to zero and attempt to solve:

Simplifying
7 + 3t = 0

Solving
7 + 3t = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3t = 0 + -7
3t = 0 + -7

Combine like terms: 0 + -7 = -7
3t = -7

Divide each side by '3'.
t = -2.333333333

Simplifying
t = -2.333333333
Solution
t = {-6, -2.333333333}