10t+5t^2=0

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

Simplifying
10t + 5t2 = 0

Solving
10t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5t'.
5t(2 + t) = 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 '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 0

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

Add '-2' to each side of the equation.
2 + -2 + t = 0 + -2

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

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

Simplifying
t = -2
Solution
t = {0, -2}