16t^2+40t+4=0

Solution for 16t^2+40t+4=0 equation:

Simplifying
16t2 + 40t + 4 = 0

Reorder the terms:
4 + 40t + 16t2 = 0

Solving
4 + 40t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 10t + 4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 10t + 4t2)' equal to zero and attempt to solve:

Simplifying
1 + 10t + 4t2 = 0

Solving
1 + 10t + 4t2 = 0

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

Divide each side by '4'.
0.25 + 2.5t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 2.5t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 2.5t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 2.5t + t2 = 0 + -0.25
2.5t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
2.5t + t2 = -0.25

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 = -0.25 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = -0.25 + 1.5625

Combine like terms: -0.25 + 1.5625 = 1.3125
1.5625 + 2.5t + t2 = 1.3125

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(t + 1.25) equal to 1.145643924 and -1.145643924.

Subproblem 1
t + 1.25 = 1.145643924

Simplifying
t + 1.25 = 1.145643924

Reorder the terms:
1.25 + t = 1.145643924

Solving
1.25 + t = 1.145643924

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 = 1.145643924 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = 1.145643924 + -1.25
t = 1.145643924 + -1.25

Combine like terms: 1.145643924 + -1.25 = -0.104356076
t = -0.104356076

Simplifying
t = -0.104356076

Subproblem 2
t + 1.25 = -1.145643924

Simplifying
t + 1.25 = -1.145643924

Reorder the terms:
1.25 + t = -1.145643924

Solving
1.25 + t = -1.145643924

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 = -1.145643924 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = -1.145643924 + -1.25
t = -1.145643924 + -1.25

Combine like terms: -1.145643924 + -1.25 = -2.395643924
t = -2.395643924

Simplifying
t = -2.395643924

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.104356076, -2.395643924}
Solution
t = {-0.104356076, -2.395643924}