10t^2=-5t

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

Simplifying
10t2 = -5t

Solving
10t2 = -5t

Solving for variable 't'.

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

Combine like terms: -5t + 5t = 0
5t + 10t2 = 0

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}