-2(8t^2-48t-8)=0

Solution for -2(8t^2-48t-8)=0 equation:

Simplifying
-2(8t2 + -48t + -8) = 0

Reorder the terms:
-2(-8 + -48t + 8t2) = 0
(-8 * -2 + -48t * -2 + 8t2 * -2) = 0
(16 + 96t + -16t2) = 0

Solving
16 + 96t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(1 + 6t + -1t2) = 0

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

Simplifying
1 + 6t + -1t2 = 0

Solving
1 + 6t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -6t + t2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -6t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + -6t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6t + t2 = 0 + 1
-6t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6t + t2 = 1

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 = 1 + 9

Reorder the terms:
9 + -6t + t2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + -6t + t2 = 10

Factor a perfect square on the left side:
(t + -3)(t + -3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(t + -3) equal to 3.16227766 and -3.16227766.

Subproblem 1
t + -3 = 3.16227766

Simplifying
t + -3 = 3.16227766

Reorder the terms:
-3 + t = 3.16227766

Solving
-3 + t = 3.16227766

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 = 3.16227766 + 3

Combine like terms: -3 + 3 = 0
0 + t = 3.16227766 + 3
t = 3.16227766 + 3

Combine like terms: 3.16227766 + 3 = 6.16227766
t = 6.16227766

Simplifying
t = 6.16227766

Subproblem 2
t + -3 = -3.16227766

Simplifying
t + -3 = -3.16227766

Reorder the terms:
-3 + t = -3.16227766

Solving
-3 + t = -3.16227766

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 = -3.16227766 + 3

Combine like terms: -3 + 3 = 0
0 + t = -3.16227766 + 3
t = -3.16227766 + 3

Combine like terms: -3.16227766 + 3 = -0.16227766
t = -0.16227766

Simplifying
t = -0.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.16227766, -0.16227766}
Solution
t = {6.16227766, -0.16227766}