2t(4t+1)=0

Solution for 2t(4t+1)=0 equation:

Simplifying
2t(4t + 1) = 0

Reorder the terms:
2t(1 + 4t) = 0
(1 * 2t + 4t * 2t) = 0
(2t + 8t2) = 0

Solving
2t + 8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2t'.
2t(1 + 4t) = 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 '(1 + 4t)' equal to zero and attempt to solve:

Simplifying
1 + 4t = 0

Solving
1 + 4t = 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 + 4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4t = 0 + -1
4t = 0 + -1

Combine like terms: 0 + -1 = -1
4t = -1

Divide each side by '4'.
t = -0.25

Simplifying
t = -0.25
Solution
t = {0, -0.25}