16t^2+192t+64=0

Solution for 16t^2+192t+64=0 equation:

Simplifying
16t2 + 192t + 64 = 0

Reorder the terms:
64 + 192t + 16t2 = 0

Solving
64 + 192t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(4 + 12t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(4 + 12t + t2)' equal to zero and attempt to solve:

Simplifying
4 + 12t + t2 = 0

Solving
4 + 12t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 12t + -4 + t2 = 0 + -4

Reorder the terms:
4 + -4 + 12t + t2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 12t + t2 = 0 + -4
12t + t2 = 0 + -4

Combine like terms: 0 + -4 = -4
12t + t2 = -4

The t term is 12t.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12t + 36 + t2 = -4 + 36

Reorder the terms:
36 + 12t + t2 = -4 + 36

Combine like terms: -4 + 36 = 32
36 + 12t + t2 = 32

Factor a perfect square on the left side:
(t + 6)(t + 6) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(t + 6) equal to 5.656854249 and -5.656854249.

Subproblem 1
t + 6 = 5.656854249

Simplifying
t + 6 = 5.656854249

Reorder the terms:
6 + t = 5.656854249

Solving
6 + t = 5.656854249

Solving for variable 't'.

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

Add '-6' to each side of the equation.
6 + -6 + t = 5.656854249 + -6

Combine like terms: 6 + -6 = 0
0 + t = 5.656854249 + -6
t = 5.656854249 + -6

Combine like terms: 5.656854249 + -6 = -0.343145751
t = -0.343145751

Simplifying
t = -0.343145751

Subproblem 2
t + 6 = -5.656854249

Simplifying
t + 6 = -5.656854249

Reorder the terms:
6 + t = -5.656854249

Solving
6 + t = -5.656854249

Solving for variable 't'.

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

Add '-6' to each side of the equation.
6 + -6 + t = -5.656854249 + -6

Combine like terms: 6 + -6 = 0
0 + t = -5.656854249 + -6
t = -5.656854249 + -6

Combine like terms: -5.656854249 + -6 = -11.656854249
t = -11.656854249

Simplifying
t = -11.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.343145751, -11.656854249}
Solution
t = {-0.343145751, -11.656854249}