-16t^2+104t+56=104

Solution for -16t^2+104t+56=104 equation:

Simplifying
-16t2 + 104t + 56 = 104

Reorder the terms:
56 + 104t + -16t2 = 104

Solving
56 + 104t + -16t2 = 104

Solving for variable 't'.

Reorder the terms:
56 + -104 + 104t + -16t2 = 104 + -104

Combine like terms: 56 + -104 = -48
-48 + 104t + -16t2 = 104 + -104

Combine like terms: 104 + -104 = 0
-48 + 104t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + 13t + -2t2) = 0

Factor a trinomial.
8((-6 + t)(1 + -2t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-6 + t)' equal to zero and attempt to solve:

Simplifying
-6 + t = 0

Solving
-6 + t = 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 + t = 0 + 6

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

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

Simplifying
t = 6
Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 0

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

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

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {6, 0.5}