(2t-5)(2t-1)=0

Solution for (2t-5)(2t-1)=0 equation:

Simplifying
(2t + -5)(2t + -1) = 0

Reorder the terms:
(-5 + 2t)(2t + -1) = 0

Reorder the terms:
(-5 + 2t)(-1 + 2t) = 0

Multiply (-5 + 2t) * (-1 + 2t)
(-5(-1 + 2t) + 2t * (-1 + 2t)) = 0
((-1 * -5 + 2t * -5) + 2t * (-1 + 2t)) = 0
((5 + -10t) + 2t * (-1 + 2t)) = 0
(5 + -10t + (-1 * 2t + 2t * 2t)) = 0
(5 + -10t + (-2t + 4t2)) = 0

Combine like terms: -10t + -2t = -12t
(5 + -12t + 4t2) = 0

Solving
5 + -12t + 4t2 = 0

Solving for variable 't'.

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

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

Simplifying
1 + -2t = 0

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

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
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 = {0.5, 2.5}