384=96+144t-16t^2

Solution for 384=96+144t-16t^2 equation:

Simplifying
384 = 96 + 144t + -16t2

Solving
384 = 96 + 144t + -16t2

Solving for variable 't'.

Combine like terms: 384 + -96 = 288
288 + -144t + 16t2 = 96 + 144t + -16t2 + -96 + -144t + 16t2

Reorder the terms:
288 + -144t + 16t2 = 96 + -96 + 144t + -144t + -16t2 + 16t2

Combine like terms: 96 + -96 = 0
288 + -144t + 16t2 = 0 + 144t + -144t + -16t2 + 16t2
288 + -144t + 16t2 = 144t + -144t + -16t2 + 16t2

Combine like terms: 144t + -144t = 0
288 + -144t + 16t2 = 0 + -16t2 + 16t2
288 + -144t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
288 + -144t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(18 + -9t + t2) = 0

Factor a trinomial.
16((3 + -1t)(6 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
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 = {3, 6}