112=-16t^2+64t+192

Solution for 112=-16t^2+64t+192 equation:

Simplifying
112 = -16t2 + 64t + 192

Reorder the terms:
112 = 192 + 64t + -16t2

Solving
112 = 192 + 64t + -16t2

Solving for variable 't'.

Combine like terms: 112 + -192 = -80
-80 + -64t + 16t2 = 192 + 64t + -16t2 + -192 + -64t + 16t2

Reorder the terms:
-80 + -64t + 16t2 = 192 + -192 + 64t + -64t + -16t2 + 16t2

Combine like terms: 192 + -192 = 0
-80 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2
-80 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2

Combine like terms: 64t + -64t = 0
-80 + -64t + 16t2 = 0 + -16t2 + 16t2
-80 + -64t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-80 + -64t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-5 + -4t + t2) = 0

Factor a trinomial.
16((-1 + -1t)(5 + -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 '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-1, 5}