16t^2+80t+6=0

Solution for 16t^2+80t+6=0 equation:

Simplifying
16t2 + 80t + 6 = 0

Reorder the terms:
6 + 80t + 16t2 = 0

Solving
6 + 80t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 40t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 40t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + 40t + 8t2 = 0

Solving
3 + 40t + 8t2 = 0

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

Divide each side by '8'.
0.375 + 5t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 5t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 5t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 5t + t2 = 0 + -0.375
5t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
5t + t2 = -0.375

The t term is 5t.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5t + 6.25 + t2 = -0.375 + 6.25

Reorder the terms:
6.25 + 5t + t2 = -0.375 + 6.25

Combine like terms: -0.375 + 6.25 = 5.875
6.25 + 5t + t2 = 5.875

Factor a perfect square on the left side:
(t + 2.5)(t + 2.5) = 5.875

Calculate the square root of the right side: 2.423839929

Break this problem into two subproblems by setting 
(t + 2.5) equal to 2.423839929 and -2.423839929.

Subproblem 1
t + 2.5 = 2.423839929

Simplifying
t + 2.5 = 2.423839929

Reorder the terms:
2.5 + t = 2.423839929

Solving
2.5 + t = 2.423839929

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = 2.423839929 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = 2.423839929 + -2.5
t = 2.423839929 + -2.5

Combine like terms: 2.423839929 + -2.5 = -0.076160071
t = -0.076160071

Simplifying
t = -0.076160071

Subproblem 2
t + 2.5 = -2.423839929

Simplifying
t + 2.5 = -2.423839929

Reorder the terms:
2.5 + t = -2.423839929

Solving
2.5 + t = -2.423839929

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = -2.423839929 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = -2.423839929 + -2.5
t = -2.423839929 + -2.5

Combine like terms: -2.423839929 + -2.5 = -4.923839929
t = -4.923839929

Simplifying
t = -4.923839929

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.076160071, -4.923839929}
Solution
t = {-0.076160071, -4.923839929}