-16t^2-48t+64=6

Solution for -16t^2-48t+64=6 equation:

Simplifying
-16t2 + -48t + 64 = 6

Reorder the terms:
64 + -48t + -16t2 = 6

Solving
64 + -48t + -16t2 = 6

Solving for variable 't'.

Reorder the terms:
64 + -6 + -48t + -16t2 = 6 + -6

Combine like terms: 64 + -6 = 58
58 + -48t + -16t2 = 6 + -6

Combine like terms: 6 + -6 = 0
58 + -48t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + -24t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(29 + -24t + -8t2)' equal to zero and attempt to solve:

Simplifying
29 + -24t + -8t2 = 0

Solving
29 + -24t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-3.625 + 3t + t2 = 0

Move the constant term to the right:

Add '3.625' to each side of the equation.
-3.625 + 3t + 3.625 + t2 = 0 + 3.625

Reorder the terms:
-3.625 + 3.625 + 3t + t2 = 0 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + 3t + t2 = 0 + 3.625
3t + t2 = 0 + 3.625

Combine like terms: 0 + 3.625 = 3.625
3t + t2 = 3.625

The t term is 3t.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3t + 2.25 + t2 = 3.625 + 2.25

Reorder the terms:
2.25 + 3t + t2 = 3.625 + 2.25

Combine like terms: 3.625 + 2.25 = 5.875
2.25 + 3t + t2 = 5.875

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 5.875

Calculate the square root of the right side: 2.423839929

Break this problem into two subproblems by setting 
(t + 1.5) equal to 2.423839929 and -2.423839929.

Subproblem 1
t + 1.5 = 2.423839929

Simplifying
t + 1.5 = 2.423839929

Reorder the terms:
1.5 + t = 2.423839929

Solving
1.5 + t = 2.423839929

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = 2.423839929 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 2.423839929 + -1.5
t = 2.423839929 + -1.5

Combine like terms: 2.423839929 + -1.5 = 0.923839929
t = 0.923839929

Simplifying
t = 0.923839929

Subproblem 2
t + 1.5 = -2.423839929

Simplifying
t + 1.5 = -2.423839929

Reorder the terms:
1.5 + t = -2.423839929

Solving
1.5 + t = -2.423839929

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = -2.423839929 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = -2.423839929 + -1.5
t = -2.423839929 + -1.5

Combine like terms: -2.423839929 + -1.5 = -3.923839929
t = -3.923839929

Simplifying
t = -3.923839929

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.923839929, -3.923839929}
Solution
t = {0.923839929, -3.923839929}