144=-16t^2+72t+288

Solution for 144=-16t^2+72t+288 equation:

Simplifying
144 = -16t2 + 72t + 288

Reorder the terms:
144 = 288 + 72t + -16t2

Solving
144 = 288 + 72t + -16t2

Solving for variable 't'.

Combine like terms: 144 + -288 = -144
-144 + -72t + 16t2 = 288 + 72t + -16t2 + -288 + -72t + 16t2

Reorder the terms:
-144 + -72t + 16t2 = 288 + -288 + 72t + -72t + -16t2 + 16t2

Combine like terms: 288 + -288 = 0
-144 + -72t + 16t2 = 0 + 72t + -72t + -16t2 + 16t2
-144 + -72t + 16t2 = 72t + -72t + -16t2 + 16t2

Combine like terms: 72t + -72t = 0
-144 + -72t + 16t2 = 0 + -16t2 + 16t2
-144 + -72t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-144 + -72t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-18 + -9t + 2t2) = 0

Factor a trinomial.
8((-3 + -2t)(6 + -1t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-3 + -2t)' equal to zero and attempt to solve:

Simplifying
-3 + -2t = 0

Solving
-3 + -2t = 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 + -2t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2t = 0 + 3
-2t = 0 + 3

Combine like terms: 0 + 3 = 3
-2t = 3

Divide each side by '-2'.
t = -1.5

Simplifying
t = -1.5
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 = {-1.5, 6}