10t^2-5t=0

Solution for 10t^2-5t=0 equation:

Simplifying
10t2 + -5t = 0

Reorder the terms:
-5t + 10t2 = 0

Solving
-5t + 10t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5t'.
5t(-1 + 2t) = 0

Ignore the factor 5.
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 '(-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
Solution
t = {0, 0.5}