-16t^2+32t+284=0

Solution for -16t^2+32t+284=0 equation:

Simplifying
-16t2 + 32t + 284 = 0

Reorder the terms:
284 + 32t + -16t2 = 0

Solving
284 + 32t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(71 + 8t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(71 + 8t + -4t2)' equal to zero and attempt to solve:

Simplifying
71 + 8t + -4t2 = 0

Solving
71 + 8t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-17.75 + -2t + t2 = 0

Move the constant term to the right:

Add '17.75' to each side of the equation.
-17.75 + -2t + 17.75 + t2 = 0 + 17.75

Reorder the terms:
-17.75 + 17.75 + -2t + t2 = 0 + 17.75

Combine like terms: -17.75 + 17.75 = 0.00
0.00 + -2t + t2 = 0 + 17.75
-2t + t2 = 0 + 17.75

Combine like terms: 0 + 17.75 = 17.75
-2t + t2 = 17.75

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 = 17.75 + 1

Reorder the terms:
1 + -2t + t2 = 17.75 + 1

Combine like terms: 17.75 + 1 = 18.75
1 + -2t + t2 = 18.75

Factor a perfect square on the left side:
(t + -1)(t + -1) = 18.75

Calculate the square root of the right side: 4.330127019

Break this problem into two subproblems by setting 
(t + -1) equal to 4.330127019 and -4.330127019.

Subproblem 1
t + -1 = 4.330127019

Simplifying
t + -1 = 4.330127019

Reorder the terms:
-1 + t = 4.330127019

Solving
-1 + t = 4.330127019

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 = 4.330127019 + 1

Combine like terms: -1 + 1 = 0
0 + t = 4.330127019 + 1
t = 4.330127019 + 1

Combine like terms: 4.330127019 + 1 = 5.330127019
t = 5.330127019

Simplifying
t = 5.330127019

Subproblem 2
t + -1 = -4.330127019

Simplifying
t + -1 = -4.330127019

Reorder the terms:
-1 + t = -4.330127019

Solving
-1 + t = -4.330127019

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 = -4.330127019 + 1

Combine like terms: -1 + 1 = 0
0 + t = -4.330127019 + 1
t = -4.330127019 + 1

Combine like terms: -4.330127019 + 1 = -3.330127019
t = -3.330127019

Simplifying
t = -3.330127019

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.330127019, -3.330127019}
Solution
t = {5.330127019, -3.330127019}