0=-16t^2+96t-128

Solution for 0=-16t^2+96t-128 equation:

Simplifying
0 = -16t2 + 96t + -128

Reorder the terms:
0 = -128 + 96t + -16t2

Solving
0 = -128 + 96t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 128 = 128
128 + -96t + 16t2 = -128 + 96t + -16t2 + 128 + -96t + 16t2

Reorder the terms:
128 + -96t + 16t2 = -128 + 128 + 96t + -96t + -16t2 + 16t2

Combine like terms: -128 + 128 = 0
128 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
128 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
128 + -96t + 16t2 = 0 + -16t2 + 16t2
128 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
128 + -96t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(8 + -6t + t2) = 0

Factor a trinomial.
16((2 + -1t)(4 + -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 '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {2, 4}