16t^2+64t+6=0

Solution for 16t^2+64t+6=0 equation:

Simplifying
16t2 + 64t + 6 = 0

Reorder the terms:
6 + 64t + 16t2 = 0

Solving
6 + 64t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 32t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 32t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + 32t + 8t2 = 0

Solving
3 + 32t + 8t2 = 0

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

Divide each side by '8'.
0.375 + 4t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 4t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 4t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 4t + t2 = 0 + -0.375
4t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
4t + t2 = -0.375

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = -0.375 + 4

Reorder the terms:
4 + 4t + t2 = -0.375 + 4

Combine like terms: -0.375 + 4 = 3.625
4 + 4t + t2 = 3.625

Factor a perfect square on the left side:
(t + 2)(t + 2) = 3.625

Calculate the square root of the right side: 1.903943276

Break this problem into two subproblems by setting 
(t + 2) equal to 1.903943276 and -1.903943276.

Subproblem 1
t + 2 = 1.903943276

Simplifying
t + 2 = 1.903943276

Reorder the terms:
2 + t = 1.903943276

Solving
2 + t = 1.903943276

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 1.903943276 + -2

Combine like terms: 2 + -2 = 0
0 + t = 1.903943276 + -2
t = 1.903943276 + -2

Combine like terms: 1.903943276 + -2 = -0.096056724
t = -0.096056724

Simplifying
t = -0.096056724

Subproblem 2
t + 2 = -1.903943276

Simplifying
t + 2 = -1.903943276

Reorder the terms:
2 + t = -1.903943276

Solving
2 + t = -1.903943276

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -1.903943276 + -2

Combine like terms: 2 + -2 = 0
0 + t = -1.903943276 + -2
t = -1.903943276 + -2

Combine like terms: -1.903943276 + -2 = -3.903943276
t = -3.903943276

Simplifying
t = -3.903943276

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.096056724, -3.903943276}
Solution
t = {-0.096056724, -3.903943276}