16t^2+48t+6=0

Solution for 16t^2+48t+6=0 equation:

Simplifying
16t2 + 48t + 6 = 0

Reorder the terms:
6 + 48t + 16t2 = 0

Solving
6 + 48t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 24t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 24t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + 24t + 8t2 = 0

Solving
3 + 24t + 8t2 = 0

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

Divide each side by '8'.
0.375 + 3t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 3t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 3t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 3t + t2 = 0 + -0.375
3t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
3t + t2 = -0.375

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 = -0.375 + 2.25

Reorder the terms:
2.25 + 3t + t2 = -0.375 + 2.25

Combine like terms: -0.375 + 2.25 = 1.875
2.25 + 3t + t2 = 1.875

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 1.875

Calculate the square root of the right side: 1.369306394

Break this problem into two subproblems by setting 
(t + 1.5) equal to 1.369306394 and -1.369306394.

Subproblem 1
t + 1.5 = 1.369306394

Simplifying
t + 1.5 = 1.369306394

Reorder the terms:
1.5 + t = 1.369306394

Solving
1.5 + t = 1.369306394

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 = 1.369306394 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 1.369306394 + -1.5
t = 1.369306394 + -1.5

Combine like terms: 1.369306394 + -1.5 = -0.130693606
t = -0.130693606

Simplifying
t = -0.130693606

Subproblem 2
t + 1.5 = -1.369306394

Simplifying
t + 1.5 = -1.369306394

Reorder the terms:
1.5 + t = -1.369306394

Solving
1.5 + t = -1.369306394

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 = -1.369306394 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = -1.369306394 + -1.5
t = -1.369306394 + -1.5

Combine like terms: -1.369306394 + -1.5 = -2.869306394
t = -2.869306394

Simplifying
t = -2.869306394

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.130693606, -2.869306394}
Solution
t = {-0.130693606, -2.869306394}