0=-16t^2+92t+24

Solution for 0=-16t^2+92t+24 equation:

Simplifying
0 = -16t2 + 92t + 24

Reorder the terms:
0 = 24 + 92t + -16t2

Solving
0 = 24 + 92t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -24 = -24
-24 + -92t + 16t2 = 24 + 92t + -16t2 + -24 + -92t + 16t2

Reorder the terms:
-24 + -92t + 16t2 = 24 + -24 + 92t + -92t + -16t2 + 16t2

Combine like terms: 24 + -24 = 0
-24 + -92t + 16t2 = 0 + 92t + -92t + -16t2 + 16t2
-24 + -92t + 16t2 = 92t + -92t + -16t2 + 16t2

Combine like terms: 92t + -92t = 0
-24 + -92t + 16t2 = 0 + -16t2 + 16t2
-24 + -92t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-24 + -92t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -23t + 4t2) = 0

Factor a trinomial.
4((-1 + -4t)(6 + -1t)) = 0

Ignore the factor 4.
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 '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 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 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {-0.25, 6}