0=-16t^2+32t+256

Solution for 0=-16t^2+32t+256 equation:

Simplifying
0 = -16t2 + 32t + 256

Reorder the terms:
0 = 256 + 32t + -16t2

Solving
0 = 256 + 32t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -256 = -256
-256 + -32t + 16t2 = 256 + 32t + -16t2 + -256 + -32t + 16t2

Reorder the terms:
-256 + -32t + 16t2 = 256 + -256 + 32t + -32t + -16t2 + 16t2

Combine like terms: 256 + -256 = 0
-256 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2
-256 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-256 + -32t + 16t2 = 0 + -16t2 + 16t2
-256 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-256 + -32t + 16t2 = 0

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

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

Simplifying
-16 + -2t + t2 = 0

Solving
-16 + -2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -2t + 16 + t2 = 0 + 16

Reorder the terms:
-16 + 16 + -2t + t2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -2t + t2 = 0 + 16
-2t + t2 = 0 + 16

Combine like terms: 0 + 16 = 16
-2t + t2 = 16

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 = 16 + 1

Reorder the terms:
1 + -2t + t2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + -2t + t2 = 17

Factor a perfect square on the left side:
(t + -1)(t + -1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(t + -1) equal to 4.123105626 and -4.123105626.

Subproblem 1
t + -1 = 4.123105626

Simplifying
t + -1 = 4.123105626

Reorder the terms:
-1 + t = 4.123105626

Solving
-1 + t = 4.123105626

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 = 4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + t = 4.123105626 + 1
t = 4.123105626 + 1

Combine like terms: 4.123105626 + 1 = 5.123105626
t = 5.123105626

Simplifying
t = 5.123105626

Subproblem 2
t + -1 = -4.123105626

Simplifying
t + -1 = -4.123105626

Reorder the terms:
-1 + t = -4.123105626

Solving
-1 + t = -4.123105626

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 = -4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + t = -4.123105626 + 1
t = -4.123105626 + 1

Combine like terms: -4.123105626 + 1 = -3.123105626
t = -3.123105626

Simplifying
t = -3.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.123105626, -3.123105626}
Solution
t = {5.123105626, -3.123105626}