0=16t^2-112t-128

Solution for 0=16t^2-112t-128 equation:

Simplifying
0 = 16t2 + -112t + -128

Reorder the terms:
0 = -128 + -112t + 16t2

Solving
0 = -128 + -112t + 16t2

Solving for variable 't'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '16'.
16(8 + 7t + -1t2) = 0

Factor a trinomial.
16((8 + -1t)(1 + t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
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 = {8, -1}