0=-16t^2+48t+288

Solution for 0=-16t^2+48t+288 equation:

Simplifying
0 = -16t2 + 48t + 288

Reorder the terms:
0 = 288 + 48t + -16t2

Solving
0 = 288 + 48t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -288 = -288
-288 + -48t + 16t2 = 288 + 48t + -16t2 + -288 + -48t + 16t2

Reorder the terms:
-288 + -48t + 16t2 = 288 + -288 + 48t + -48t + -16t2 + 16t2

Combine like terms: 288 + -288 = 0
-288 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2
-288 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
-288 + -48t + 16t2 = 0 + -16t2 + 16t2
-288 + -48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-288 + -48t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-18 + -3t + 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}