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

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

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

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

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

Multiply (3 + 4t) * (3 + t)
(3(3 + t) + 4t * (3 + t)) = 0
((3 * 3 + t * 3) + 4t * (3 + t)) = 0
((9 + 3t) + 4t * (3 + t)) = 0
(9 + 3t + (3 * 4t + t * 4t)) = 0
(9 + 3t + (12t + 4t2)) = 0

Combine like terms: 3t + 12t = 15t
(9 + 15t + 4t2) = 0

Solving
9 + 15t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + t)(3 + 4t) = 0

Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

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

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

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

Simplifying
t = -3
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 = {-3, -0.75}