116=-16t^2+38t+104

Solution for 116=-16t^2+38t+104 equation:

Simplifying
116 = -16t2 + 38t + 104

Reorder the terms:
116 = 104 + 38t + -16t2

Solving
116 = 104 + 38t + -16t2

Solving for variable 't'.

Combine like terms: 116 + -104 = 12
12 + -38t + 16t2 = 104 + 38t + -16t2 + -104 + -38t + 16t2

Reorder the terms:
12 + -38t + 16t2 = 104 + -104 + 38t + -38t + -16t2 + 16t2

Combine like terms: 104 + -104 = 0
12 + -38t + 16t2 = 0 + 38t + -38t + -16t2 + 16t2
12 + -38t + 16t2 = 38t + -38t + -16t2 + 16t2

Combine like terms: 38t + -38t = 0
12 + -38t + 16t2 = 0 + -16t2 + 16t2
12 + -38t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
12 + -38t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -19t + 8t2) = 0

Factor a trinomial.
2((3 + -8t)(2 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -8t)' equal to zero and attempt to solve:

Simplifying
3 + -8t = 0

Solving
3 + -8t = 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 + -8t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8t = 0 + -3
-8t = 0 + -3

Combine like terms: 0 + -3 = -3
-8t = -3

Divide each side by '-8'.
t = 0.375

Simplifying
t = 0.375
Subproblem 2
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
Solution
t = {0.375, 2}