8=-16t^2+12t+6

Solution for 8=-16t^2+12t+6 equation:

Simplifying
8 = -16t2 + 12t + 6

Reorder the terms:
8 = 6 + 12t + -16t2

Solving
8 = 6 + 12t + -16t2

Solving for variable 't'.

Combine like terms: 8 + -6 = 2
2 + -12t + 16t2 = 6 + 12t + -16t2 + -6 + -12t + 16t2

Reorder the terms:
2 + -12t + 16t2 = 6 + -6 + 12t + -12t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
2 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2
2 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2

Combine like terms: 12t + -12t = 0
2 + -12t + 16t2 = 0 + -16t2 + 16t2
2 + -12t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
2 + -12t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6t + 8t2) = 0

Factor a trinomial.
2((1 + -4t)(1 + -2t)) = 0

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

Simplifying
1 + -4t = 0

Solving
1 + -4t = 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 + -4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t = 0 + -1
-4t = 0 + -1

Combine like terms: 0 + -1 = -1
-4t = -1

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25
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 = {0.25, 0.5}