144=-16t^2+96t+256

Solution for 144=-16t^2+96t+256 equation:

Simplifying
144 = -16t2 + 96t + 256

Reorder the terms:
144 = 256 + 96t + -16t2

Solving
144 = 256 + 96t + -16t2

Solving for variable 't'.

Combine like terms: 144 + -256 = -112
-112 + -96t + 16t2 = 256 + 96t + -16t2 + -256 + -96t + 16t2

Reorder the terms:
-112 + -96t + 16t2 = 256 + -256 + 96t + -96t + -16t2 + 16t2

Combine like terms: 256 + -256 = 0
-112 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
-112 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
-112 + -96t + 16t2 = 0 + -16t2 + 16t2
-112 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-112 + -96t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-7 + -6t + t2) = 0

Factor a trinomial.
16((-1 + -1t)(7 + -1t)) = 0

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

Simplifying
-1 + -1t = 0

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

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

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

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

Simplifying
t = -1
Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {-1, 7}