t(2t-5)=0

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

Simplifying
t(2t + -5) = 0

Reorder the terms:
t(-5 + 2t) = 0
(-5 * t + 2t * t) = 0
(-5t + 2t2) = 0

Solving
-5t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-5 + 2t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
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, 2.5}