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 + t2) = 0

Factor a trinomial.
16((-1 + -1t)(8 + -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 '(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
Solution
t = {-1, 8}