(2t-5)(3t-6)=0

Solution for (2t-5)(3t-6)=0 equation:

Simplifying
(2t + -5)(3t + -6) = 0

Reorder the terms:
(-5 + 2t)(3t + -6) = 0

Reorder the terms:
(-5 + 2t)(-6 + 3t) = 0

Multiply (-5 + 2t) * (-6 + 3t)
(-5(-6 + 3t) + 2t * (-6 + 3t)) = 0
((-6 * -5 + 3t * -5) + 2t * (-6 + 3t)) = 0
((30 + -15t) + 2t * (-6 + 3t)) = 0
(30 + -15t + (-6 * 2t + 3t * 2t)) = 0
(30 + -15t + (-12t + 6t2)) = 0

Combine like terms: -15t + -12t = -27t
(30 + -27t + 6t2) = 0

Solving
30 + -27t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -9t + 2t2) = 0

Factor a trinomial.
3((2 + -1t)(5 + -2t)) = 0

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {2, 2.5}