2t^2+10t=0

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

Simplifying
2t2 + 10t = 0

Reorder the terms:
10t + 2t2 = 0

Solving
10t + 2t2 = 0

Solving for variable 't'.

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

Ignore the factor 2.
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 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

Solving
5 + t = 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 + t = 0 + -5

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

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

Simplifying
t = -5
Solution
t = {0, -5}