-16t^2+64t+8-68=0

Solution for -16t^2+64t+8-68=0 equation:

Simplifying
-16t2 + 64t + 8 + -68 = 0

Reorder the terms:
8 + -68 + 64t + -16t2 = 0

Combine like terms: 8 + -68 = -60
-60 + 64t + -16t2 = 0

Solving
-60 + 64t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 16t + -4t2) = 0

Factor a trinomial.
4((-5 + 2t)(3 + -2t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + 2t)' equal to zero and attempt to solve:

Simplifying
-5 + 2t = 0

Solving
-5 + 2t = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2t = 0 + 5
2t = 0 + 5

Combine like terms: 0 + 5 = 5
2t = 5

Divide each side by '2'.
t = 2.5

Simplifying
t = 2.5
Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {2.5, 1.5}