0=16t^2+8t+1

Solution for 0=16t^2+8t+1 equation:

Simplifying
0 = 16t2 + 8t + 1

Reorder the terms:
0 = 1 + 8t + 16t2

Solving
0 = 1 + 8t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -1 = -1
-1 + -8t + -16t2 = 1 + 8t + 16t2 + -1 + -8t + -16t2

Reorder the terms:
-1 + -8t + -16t2 = 1 + -1 + 8t + -8t + 16t2 + -16t2

Combine like terms: 1 + -1 = 0
-1 + -8t + -16t2 = 0 + 8t + -8t + 16t2 + -16t2
-1 + -8t + -16t2 = 8t + -8t + 16t2 + -16t2

Combine like terms: 8t + -8t = 0
-1 + -8t + -16t2 = 0 + 16t2 + -16t2
-1 + -8t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-1 + -8t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 8t + 16t2) = 0

Factor a trinomial.
-1((1 + 4t)(1 + 4t)) = 0

Ignore the factor -1.
Subproblem 1
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
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 = {-0.25, -0.25}