0=-16t^2+80t-96

Solution for 0=-16t^2+80t-96 equation:

Simplifying
0 = -16t2 + 80t + -96

Reorder the terms:
0 = -96 + 80t + -16t2

Solving
0 = -96 + 80t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 96 = 96
96 + -80t + 16t2 = -96 + 80t + -16t2 + 96 + -80t + 16t2

Reorder the terms:
96 + -80t + 16t2 = -96 + 96 + 80t + -80t + -16t2 + 16t2

Combine like terms: -96 + 96 = 0
96 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2
96 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2

Combine like terms: 80t + -80t = 0
96 + -80t + 16t2 = 0 + -16t2 + 16t2
96 + -80t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
96 + -80t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(6 + -5t + 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}