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

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

Simplifying
0 = -16t2 + 16t + 96

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

Solving
0 = 96 + 16t + -16t2

Solving for variable 't'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '16'.
16(-6 + -1t + t2) = 0

Factor a trinomial.
16((-2 + -1t)(3 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve:

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-2, 3}