-16t^2+56t+32=0

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

Simplifying
-16t2 + 56t + 32 = 0

Reorder the terms:
32 + 56t + -16t2 = 0

Solving
32 + 56t + -16t2 = 0

Solving for variable 't'.

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

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

Ignore the factor 8.
Subproblem 1
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
Subproblem 2
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
Solution
t = {4, -0.5}