-16t^2+24t+6=14

Solution for -16t^2+24t+6=14 equation:

Simplifying
-16t2 + 24t + 6 = 14

Reorder the terms:
6 + 24t + -16t2 = 14

Solving
6 + 24t + -16t2 = 14

Solving for variable 't'.

Reorder the terms:
6 + -14 + 24t + -16t2 = 14 + -14

Combine like terms: 6 + -14 = -8
-8 + 24t + -16t2 = 14 + -14

Combine like terms: 14 + -14 = 0
-8 + 24t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + 3t + -2t2) = 0

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

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

Simplifying
-1 + t = 0

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

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

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

Simplifying
t = 1
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 = {1, 0.5}