t(2t+1)=0

Solution for t(2t+1)=0 equation:

Simplifying
t(2t + 1) = 0

Reorder the terms:
t(1 + 2t) = 0
(1 * t + 2t * t) = 0
(1t + 2t2) = 0

Solving
1t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(1 + 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 '(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}