-16t^2+32t+136=0

Solution for -16t^2+32t+136=0 equation:

Simplifying
-16t2 + 32t + 136 = 0

Reorder the terms:
136 + 32t + -16t2 = 0

Solving
136 + 32t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(17 + 4t + -2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(17 + 4t + -2t2)' equal to zero and attempt to solve:

Simplifying
17 + 4t + -2t2 = 0

Solving
17 + 4t + -2t2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-8.5 + -2t + t2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + -2t + 8.5 + t2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + -2t + t2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + -2t + t2 = 0 + 8.5
-2t + t2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
-2t + t2 = 8.5

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 = 8.5 + 1

Reorder the terms:
1 + -2t + t2 = 8.5 + 1

Combine like terms: 8.5 + 1 = 9.5
1 + -2t + t2 = 9.5

Factor a perfect square on the left side:
(t + -1)(t + -1) = 9.5

Calculate the square root of the right side: 3.082207001

Break this problem into two subproblems by setting 
(t + -1) equal to 3.082207001 and -3.082207001.

Subproblem 1
t + -1 = 3.082207001

Simplifying
t + -1 = 3.082207001

Reorder the terms:
-1 + t = 3.082207001

Solving
-1 + t = 3.082207001

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 = 3.082207001 + 1

Combine like terms: -1 + 1 = 0
0 + t = 3.082207001 + 1
t = 3.082207001 + 1

Combine like terms: 3.082207001 + 1 = 4.082207001
t = 4.082207001

Simplifying
t = 4.082207001

Subproblem 2
t + -1 = -3.082207001

Simplifying
t + -1 = -3.082207001

Reorder the terms:
-1 + t = -3.082207001

Solving
-1 + t = -3.082207001

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 = -3.082207001 + 1

Combine like terms: -1 + 1 = 0
0 + t = -3.082207001 + 1
t = -3.082207001 + 1

Combine like terms: -3.082207001 + 1 = -2.082207001
t = -2.082207001

Simplifying
t = -2.082207001

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.082207001, -2.082207001}
Solution
t = {4.082207001, -2.082207001}