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

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

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

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

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

Multiply (3 + 4t) * (6 + t)
(3(6 + t) + 4t * (6 + t)) = 0
((6 * 3 + t * 3) + 4t * (6 + t)) = 0
((18 + 3t) + 4t * (6 + t)) = 0
(18 + 3t + (6 * 4t + t * 4t)) = 0
(18 + 3t + (24t + 4t2)) = 0

Combine like terms: 3t + 24t = 27t
(18 + 27t + 4t2) = 0

Solving
18 + 27t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(6 + t)(3 + 4t) = 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 '(3 + 4t)' equal to zero and attempt to solve:

Simplifying
3 + 4t = 0

Solving
3 + 4t = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4t = 0 + -3
4t = 0 + -3

Combine like terms: 0 + -3 = -3
4t = -3

Divide each side by '4'.
t = -0.75

Simplifying
t = -0.75
Solution
t = {-6, -0.75}