0=-16t^2+96t-96

Solution for 0=-16t^2+96t-96 equation:

Simplifying
0 = -16t2 + 96t + -96

Reorder the terms:
0 = -96 + 96t + -16t2

Solving
0 = -96 + 96t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 96 = 96
96 + -96t + 16t2 = -96 + 96t + -16t2 + 96 + -96t + 16t2

Reorder the terms:
96 + -96t + 16t2 = -96 + 96 + 96t + -96t + -16t2 + 16t2

Combine like terms: -96 + 96 = 0
96 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
96 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
96 + -96t + 16t2 = 0 + -16t2 + 16t2
96 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
96 + -96t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(6 + -6t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(6 + -6t + t2)' equal to zero and attempt to solve:

Simplifying
6 + -6t + t2 = 0

Solving
6 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -6t + -6 + t2 = 0 + -6

Reorder the terms:
6 + -6 + -6t + t2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -6t + t2 = 0 + -6
-6t + t2 = 0 + -6

Combine like terms: 0 + -6 = -6
-6t + t2 = -6

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = -6 + 9

Reorder the terms:
9 + -6t + t2 = -6 + 9

Combine like terms: -6 + 9 = 3
9 + -6t + t2 = 3

Factor a perfect square on the left side:
(t + -3)(t + -3) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(t + -3) equal to 1.732050808 and -1.732050808.

Subproblem 1
t + -3 = 1.732050808

Simplifying
t + -3 = 1.732050808

Reorder the terms:
-3 + t = 1.732050808

Solving
-3 + t = 1.732050808

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + t = 1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + t = 1.732050808 + 3
t = 1.732050808 + 3

Combine like terms: 1.732050808 + 3 = 4.732050808
t = 4.732050808

Simplifying
t = 4.732050808

Subproblem 2
t + -3 = -1.732050808

Simplifying
t + -3 = -1.732050808

Reorder the terms:
-3 + t = -1.732050808

Solving
-3 + t = -1.732050808

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + t = -1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + t = -1.732050808 + 3
t = -1.732050808 + 3

Combine like terms: -1.732050808 + 3 = 1.267949192
t = 1.267949192

Simplifying
t = 1.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.732050808, 1.267949192}
Solution
t = {4.732050808, 1.267949192}