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

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

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

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

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

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

Combine like terms: -2t + 9t = 7t
(-3 + 7t + 6t2) = 0

Solving
-3 + 7t + 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}