(2t+3)(3t+1)=0

Solution for (2t+3)(3t+1)=0 equation:

Simplifying
(2t + 3)(3t + 1) = 0

Reorder the terms:
(3 + 2t)(3t + 1) = 0

Reorder the terms:
(3 + 2t)(1 + 3t) = 0

Multiply (3 + 2t) * (1 + 3t)
(3(1 + 3t) + 2t * (1 + 3t)) = 0
((1 * 3 + 3t * 3) + 2t * (1 + 3t)) = 0
((3 + 9t) + 2t * (1 + 3t)) = 0
(3 + 9t + (1 * 2t + 3t * 2t)) = 0
(3 + 9t + (2t + 6t2)) = 0

Combine like terms: 9t + 2t = 11t
(3 + 11t + 6t2) = 0

Solving
3 + 11t + 6t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + 2t)(1 + 3t) = 0

Subproblem 1
Set the factor '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

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

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

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

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Subproblem 2
Set the factor '(1 + 3t)' equal to zero and attempt to solve:

Simplifying
1 + 3t = 0

Solving
1 + 3t = 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 + 3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3t = 0 + -1
3t = 0 + -1

Combine like terms: 0 + -1 = -1
3t = -1

Divide each side by '3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Solution
t = {-1.5, -0.3333333333}