8=-16t^2+20t+14

Solution for 8=-16t^2+20t+14 equation:

Simplifying
8 = -16t2 + 20t + 14

Reorder the terms:
8 = 14 + 20t + -16t2

Solving
8 = 14 + 20t + -16t2

Solving for variable 't'.

Combine like terms: 8 + -14 = -6
-6 + -20t + 16t2 = 14 + 20t + -16t2 + -14 + -20t + 16t2

Reorder the terms:
-6 + -20t + 16t2 = 14 + -14 + 20t + -20t + -16t2 + 16t2

Combine like terms: 14 + -14 = 0
-6 + -20t + 16t2 = 0 + 20t + -20t + -16t2 + 16t2
-6 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2

Combine like terms: 20t + -20t = 0
-6 + -20t + 16t2 = 0 + -16t2 + 16t2
-6 + -20t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-6 + -20t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -10t + 8t2) = 0

Factor a trinomial.
2((-1 + -4t)(3 + -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 '(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 = {-0.25, 1.5}