8(t)=-16t^2+6

Solution for 8(t)=-16t^2+6 equation:

Simplifying
8(t) = -16t2 + 6

Reorder the terms:
8t = 6 + -16t2

Solving
8t = 6 + -16t2

Solving for variable 't'.

Reorder the terms:
-6 + 8t + 16t2 = 6 + -16t2 + -6 + 16t2

Reorder the terms:
-6 + 8t + 16t2 = 6 + -6 + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
-6 + 8t + 16t2 = 0 + -16t2 + 16t2
-6 + 8t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-6 + 8t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 4t + 8t2)' equal to zero and attempt to solve:

Simplifying
-3 + 4t + 8t2 = 0

Solving
-3 + 4t + 8t2 = 0

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

Divide each side by '8'.
-0.375 + 0.5t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + 0.5t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + 0.5t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 0.5t + t2 = 0 + 0.375
0.5t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
0.5t + t2 = 0.375

The t term is 0.5t.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5t + 0.0625 + t2 = 0.375 + 0.0625

Reorder the terms:
0.0625 + 0.5t + t2 = 0.375 + 0.0625

Combine like terms: 0.375 + 0.0625 = 0.4375
0.0625 + 0.5t + t2 = 0.4375

Factor a perfect square on the left side:
(t + 0.25)(t + 0.25) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(t + 0.25) equal to 0.661437828 and -0.661437828.

Subproblem 1
t + 0.25 = 0.661437828

Simplifying
t + 0.25 = 0.661437828

Reorder the terms:
0.25 + t = 0.661437828

Solving
0.25 + t = 0.661437828

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = 0.661437828 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = 0.661437828 + -0.25
t = 0.661437828 + -0.25

Combine like terms: 0.661437828 + -0.25 = 0.411437828
t = 0.411437828

Simplifying
t = 0.411437828

Subproblem 2
t + 0.25 = -0.661437828

Simplifying
t + 0.25 = -0.661437828

Reorder the terms:
0.25 + t = -0.661437828

Solving
0.25 + t = -0.661437828

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = -0.661437828 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = -0.661437828 + -0.25
t = -0.661437828 + -0.25

Combine like terms: -0.661437828 + -0.25 = -0.911437828
t = -0.911437828

Simplifying
t = -0.911437828

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.411437828, -0.911437828}
Solution
t = {0.411437828, -0.911437828}