-16t^2+32t+72=0

Solution for -16t^2+32t+72=0 equation:

Simplifying
-16t2 + 32t + 72 = 0

Reorder the terms:
72 + 32t + -16t2 = 0

Solving
72 + 32t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(9 + 4t + -2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(9 + 4t + -2t2)' equal to zero and attempt to solve:

Simplifying
9 + 4t + -2t2 = 0

Solving
9 + 4t + -2t2 = 0

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

Divide each side by '-2'.
-4.5 + -2t + t2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -2t + 4.5 + t2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -2t + t2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -2t + t2 = 0 + 4.5
-2t + t2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-2t + t2 = 4.5

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 = 4.5 + 1

Reorder the terms:
1 + -2t + t2 = 4.5 + 1

Combine like terms: 4.5 + 1 = 5.5
1 + -2t + t2 = 5.5

Factor a perfect square on the left side:
(t + -1)(t + -1) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(t + -1) equal to 2.34520788 and -2.34520788.

Subproblem 1
t + -1 = 2.34520788

Simplifying
t + -1 = 2.34520788

Reorder the terms:
-1 + t = 2.34520788

Solving
-1 + t = 2.34520788

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 = 2.34520788 + 1

Combine like terms: -1 + 1 = 0
0 + t = 2.34520788 + 1
t = 2.34520788 + 1

Combine like terms: 2.34520788 + 1 = 3.34520788
t = 3.34520788

Simplifying
t = 3.34520788

Subproblem 2
t + -1 = -2.34520788

Simplifying
t + -1 = -2.34520788

Reorder the terms:
-1 + t = -2.34520788

Solving
-1 + t = -2.34520788

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 = -2.34520788 + 1

Combine like terms: -1 + 1 = 0
0 + t = -2.34520788 + 1
t = -2.34520788 + 1

Combine like terms: -2.34520788 + 1 = -1.34520788
t = -1.34520788

Simplifying
t = -1.34520788

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.34520788, -1.34520788}
Solution
t = {3.34520788, -1.34520788}