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

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

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

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

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

Multiply (-3 + 2t) * (-2 + 3t)
(-3(-2 + 3t) + 2t * (-2 + 3t)) = 0
((-2 * -3 + 3t * -3) + 2t * (-2 + 3t)) = 0
((6 + -9t) + 2t * (-2 + 3t)) = 0
(6 + -9t + (-2 * 2t + 3t * 2t)) = 0
(6 + -9t + (-4t + 6t2)) = 0

Combine like terms: -9t + -4t = -13t
(6 + -13t + 6t2) = 0

Solving
6 + -13t + 6t2 = 0

Solving for variable 't'.

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

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

Simplifying
2 + -3t = 0

Solving
2 + -3t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3t = 0 + -2

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

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

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Subproblem 2
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
Solution
t = {0.6666666667, 1.5}