0=384+32t-16t^2

Solution for 0=384+32t-16t^2 equation:

Simplifying
0 = 384 + 32t + -16t2

Solving
0 = 384 + 32t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -384 = -384
-384 + -32t + 16t2 = 384 + 32t + -16t2 + -384 + -32t + 16t2

Reorder the terms:
-384 + -32t + 16t2 = 384 + -384 + 32t + -32t + -16t2 + 16t2

Combine like terms: 384 + -384 = 0
-384 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2
-384 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-384 + -32t + 16t2 = 0 + -16t2 + 16t2
-384 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-384 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-24 + -2t + t2) = 0

Factor a trinomial.
16((-4 + -1t)(6 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1t = 0 + 4

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

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

Divide each side by '-1'.
t = -4

Simplifying
t = -4
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 = {-4, 6}