0=32+56t-16t^2

Solution for 0=32+56t-16t^2 equation:

Simplifying
0 = 32 + 56t + -16t2

Solving
0 = 32 + 56t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -32 = -32
-32 + -56t + 16t2 = 32 + 56t + -16t2 + -32 + -56t + 16t2

Reorder the terms:
-32 + -56t + 16t2 = 32 + -32 + 56t + -56t + -16t2 + 16t2

Combine like terms: 32 + -32 = 0
-32 + -56t + 16t2 = 0 + 56t + -56t + -16t2 + 16t2
-32 + -56t + 16t2 = 56t + -56t + -16t2 + 16t2

Combine like terms: 56t + -56t = 0
-32 + -56t + 16t2 = 0 + -16t2 + 16t2
-32 + -56t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-32 + -56t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + -7t + 2t2) = 0

Factor a trinomial.
8((-1 + -2t)(4 + -1t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve:

Simplifying
-1 + -2t = 0

Solving
-1 + -2t = 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 + -2t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2t = 0 + 1
-2t = 0 + 1

Combine like terms: 0 + 1 = 1
-2t = 1

Divide each side by '-2'.
t = -0.5

Simplifying
t = -0.5
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-0.5, 4}