0=-16t^2+128t-192

Solution for 0=-16t^2+128t-192 equation:

Simplifying
0 = -16t2 + 128t + -192

Reorder the terms:
0 = -192 + 128t + -16t2

Solving
0 = -192 + 128t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 192 = 192
192 + -128t + 16t2 = -192 + 128t + -16t2 + 192 + -128t + 16t2

Reorder the terms:
192 + -128t + 16t2 = -192 + 192 + 128t + -128t + -16t2 + 16t2

Combine like terms: -192 + 192 = 0
192 + -128t + 16t2 = 0 + 128t + -128t + -16t2 + 16t2
192 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2

Combine like terms: 128t + -128t = 0
192 + -128t + 16t2 = 0 + -16t2 + 16t2
192 + -128t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
192 + -128t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(12 + -8t + t2) = 0

Factor a trinomial.
16((2 + -1t)(6 + -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 '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {2, 6}