-16t^2+192t+4=0

Solution for -16t^2+192t+4=0 equation:

Simplifying
-16t2 + 192t + 4 = 0

Reorder the terms:
4 + 192t + -16t2 = 0

Solving
4 + 192t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 48t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 48t + -4t2)' equal to zero and attempt to solve:

Simplifying
1 + 48t + -4t2 = 0

Solving
1 + 48t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -12t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -12t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -12t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -12t + t2 = 0 + 0.25
-12t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-12t + t2 = 0.25

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 = 0.25 + 36

Reorder the terms:
36 + -12t + t2 = 0.25 + 36

Combine like terms: 0.25 + 36 = 36.25
36 + -12t + t2 = 36.25

Factor a perfect square on the left side:
(t + -6)(t + -6) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(t + -6) equal to 6.020797289 and -6.020797289.

Subproblem 1
t + -6 = 6.020797289

Simplifying
t + -6 = 6.020797289

Reorder the terms:
-6 + t = 6.020797289

Solving
-6 + t = 6.020797289

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 = 6.020797289 + 6

Combine like terms: -6 + 6 = 0
0 + t = 6.020797289 + 6
t = 6.020797289 + 6

Combine like terms: 6.020797289 + 6 = 12.020797289
t = 12.020797289

Simplifying
t = 12.020797289

Subproblem 2
t + -6 = -6.020797289

Simplifying
t + -6 = -6.020797289

Reorder the terms:
-6 + t = -6.020797289

Solving
-6 + t = -6.020797289

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 = -6.020797289 + 6

Combine like terms: -6 + 6 = 0
0 + t = -6.020797289 + 6
t = -6.020797289 + 6

Combine like terms: -6.020797289 + 6 = -0.020797289
t = -0.020797289

Simplifying
t = -0.020797289

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {12.020797289, -0.020797289}
Solution
t = {12.020797289, -0.020797289}