96=-16t^2+8t+96

Solution for 96=-16t^2+8t+96 equation:

Simplifying
96 = -16t2 + 8t + 96

Reorder the terms:
96 = 96 + 8t + -16t2

Add '-96' to each side of the equation.
96 + -96 = 96 + 8t + -96 + -16t2

Combine like terms: 96 + -96 = 0
0 = 96 + 8t + -96 + -16t2

Reorder the terms:
0 = 96 + -96 + 8t + -16t2

Combine like terms: 96 + -96 = 0
0 = 0 + 8t + -16t2
0 = 8t + -16t2

Solving
0 = 8t + -16t2

Solving for variable 't'.
Remove the zero:
-8t + 16t2 = 8t + -16t2 + -8t + 16t2

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

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

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

Factor out the Greatest Common Factor (GCF), '8t'.
8t(-1 + 2t) = 0

Ignore the factor 8.
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}