16t^2+40t+6=0

Solution for 16t^2+40t+6=0 equation:

Simplifying
16t2 + 40t + 6 = 0

Reorder the terms:
6 + 40t + 16t2 = 0

Solving
6 + 40t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 20t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 20t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + 20t + 8t2 = 0

Solving
3 + 20t + 8t2 = 0

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

Divide each side by '8'.
0.375 + 2.5t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 2.5t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 2.5t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 2.5t + t2 = 0 + -0.375
2.5t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
2.5t + t2 = -0.375

The t term is 2.5t.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5t + 1.5625 + t2 = -0.375 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = -0.375 + 1.5625

Combine like terms: -0.375 + 1.5625 = 1.1875
1.5625 + 2.5t + t2 = 1.1875

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 1.1875

Calculate the square root of the right side: 1.089724736

Break this problem into two subproblems by setting 
(t + 1.25) equal to 1.089724736 and -1.089724736.

Subproblem 1
t + 1.25 = 1.089724736

Simplifying
t + 1.25 = 1.089724736

Reorder the terms:
1.25 + t = 1.089724736

Solving
1.25 + t = 1.089724736

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = 1.089724736 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = 1.089724736 + -1.25
t = 1.089724736 + -1.25

Combine like terms: 1.089724736 + -1.25 = -0.160275264
t = -0.160275264

Simplifying
t = -0.160275264

Subproblem 2
t + 1.25 = -1.089724736

Simplifying
t + 1.25 = -1.089724736

Reorder the terms:
1.25 + t = -1.089724736

Solving
1.25 + t = -1.089724736

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = -1.089724736 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = -1.089724736 + -1.25
t = -1.089724736 + -1.25

Combine like terms: -1.089724736 + -1.25 = -2.339724736
t = -2.339724736

Simplifying
t = -2.339724736

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.160275264, -2.339724736}
Solution
t = {-0.160275264, -2.339724736}