0=-16t^2+96t-108

Solution for 0=-16t^2+96t-108 equation:

Simplifying
0 = -16t2 + 96t + -108

Reorder the terms:
0 = -108 + 96t + -16t2

Solving
0 = -108 + 96t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 108 = 108
108 + -96t + 16t2 = -108 + 96t + -16t2 + 108 + -96t + 16t2

Reorder the terms:
108 + -96t + 16t2 = -108 + 108 + 96t + -96t + -16t2 + 16t2

Combine like terms: -108 + 108 = 0
108 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
108 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
108 + -96t + 16t2 = 0 + -16t2 + 16t2
108 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
108 + -96t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + -24t + 4t2) = 0

Factor a trinomial.
4((3 + -2t)(9 + -2t)) = 0

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

Simplifying
3 + -2t = 0

Solving
3 + -2t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 2
Set the factor '(9 + -2t)' equal to zero and attempt to solve:

Simplifying
9 + -2t = 0

Solving
9 + -2t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2t = 0 + -9
-2t = 0 + -9

Combine like terms: 0 + -9 = -9
-2t = -9

Divide each side by '-2'.
t = 4.5

Simplifying
t = 4.5
Solution
t = {1.5, 4.5}