112=-16t^2-128t

Solution for 112=-16t^2-128t equation:

Simplifying
112 = -16t2 + -128t

Reorder the terms:
112 = -128t + -16t2

Solving
112 = -128t + -16t2

Solving for variable 't'.

Reorder the terms:
112 + 128t + 16t2 = -128t + 128t + -16t2 + 16t2

Combine like terms: -128t + 128t = 0
112 + 128t + 16t2 = 0 + -16t2 + 16t2
112 + 128t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
112 + 128t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(7 + 8t + t2) = 0

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

Ignore the factor 16.
Subproblem 1
Set the factor '(7 + t)' equal to zero and attempt to solve:

Simplifying
7 + t = 0

Solving
7 + t = 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 + t = 0 + -7

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

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

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

Simplifying
1 + t = 0

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

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

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

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