-16t^2+32t+382=0

Solution for -16t^2+32t+382=0 equation:

Simplifying
-16t2 + 32t + 382 = 0

Reorder the terms:
382 + 32t + -16t2 = 0

Solving
382 + 32t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(191 + 16t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(191 + 16t + -8t2)' equal to zero and attempt to solve:

Simplifying
191 + 16t + -8t2 = 0

Solving
191 + 16t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-23.875 + -2t + t2 = 0

Move the constant term to the right:

Add '23.875' to each side of the equation.
-23.875 + -2t + 23.875 + t2 = 0 + 23.875

Reorder the terms:
-23.875 + 23.875 + -2t + t2 = 0 + 23.875

Combine like terms: -23.875 + 23.875 = 0.000
0.000 + -2t + t2 = 0 + 23.875
-2t + t2 = 0 + 23.875

Combine like terms: 0 + 23.875 = 23.875
-2t + t2 = 23.875

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 23.875 + 1

Reorder the terms:
1 + -2t + t2 = 23.875 + 1

Combine like terms: 23.875 + 1 = 24.875
1 + -2t + t2 = 24.875

Factor a perfect square on the left side:
(t + -1)(t + -1) = 24.875

Calculate the square root of the right side: 4.987484336

Break this problem into two subproblems by setting 
(t + -1) equal to 4.987484336 and -4.987484336.

Subproblem 1
t + -1 = 4.987484336

Simplifying
t + -1 = 4.987484336

Reorder the terms:
-1 + t = 4.987484336

Solving
-1 + t = 4.987484336

Solving for variable 't'.

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 = 4.987484336 + 1

Combine like terms: -1 + 1 = 0
0 + t = 4.987484336 + 1
t = 4.987484336 + 1

Combine like terms: 4.987484336 + 1 = 5.987484336
t = 5.987484336

Simplifying
t = 5.987484336

Subproblem 2
t + -1 = -4.987484336

Simplifying
t + -1 = -4.987484336

Reorder the terms:
-1 + t = -4.987484336

Solving
-1 + t = -4.987484336

Solving for variable 't'.

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 = -4.987484336 + 1

Combine like terms: -1 + 1 = 0
0 + t = -4.987484336 + 1
t = -4.987484336 + 1

Combine like terms: -4.987484336 + 1 = -3.987484336
t = -3.987484336

Simplifying
t = -3.987484336

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.987484336, -3.987484336}
Solution
t = {5.987484336, -3.987484336}