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

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

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

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

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

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

Combine like terms: -6t + -5t = -11t
(15 + -11t + 2t2) = 0

Solving
15 + -11t + 2t2 = 0

Solving for variable 't'.

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

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

Simplifying
3 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {2.5, 3}