-16t^2+4t+8=0

Solution for -16t^2+4t+8=0 equation:

Simplifying
-16t2 + 4t + 8 = 0

Reorder the terms:
8 + 4t + -16t2 = 0

Solving
8 + 4t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + t + -4t2)' equal to zero and attempt to solve:

Simplifying
2 + t + -4t2 = 0

Solving
2 + t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.5 + -0.25t + t2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.25t + 0.5 + t2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.25t + t2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.25t + t2 = 0 + 0.5
-0.25t + t2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.25t + t2 = 0.5

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.25t + 0.25 + t2 = 0.5 + 0.25

Reorder the terms:
0.25 + -0.25t + t2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
0.25 + -0.25t + t2 = 0.75

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(t + 0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
t + 0.5 = 0.866025404

Simplifying
t + 0.5 = 0.866025404

Reorder the terms:
0.5 + t = 0.866025404

Solving
0.5 + t = 0.866025404

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 0.866025404 + -0.5
t = 0.866025404 + -0.5

Combine like terms: 0.866025404 + -0.5 = 0.366025404
t = 0.366025404

Simplifying
t = 0.366025404

Subproblem 2
t + 0.5 = -0.866025404

Simplifying
t + 0.5 = -0.866025404

Reorder the terms:
0.5 + t = -0.866025404

Solving
0.5 + t = -0.866025404

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -0.866025404 + -0.5
t = -0.866025404 + -0.5

Combine like terms: -0.866025404 + -0.5 = -1.366025404
t = -1.366025404

Simplifying
t = -1.366025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.366025404, -1.366025404}
Solution
t = {0.366025404, -1.366025404}