0=16t^2+32t+4

Solution for 0=16t^2+32t+4 equation:

Simplifying
0 = 16t2 + 32t + 4

Reorder the terms:
0 = 4 + 32t + 16t2

Solving
0 = 4 + 32t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -4 = -4
-4 + -32t + -16t2 = 4 + 32t + 16t2 + -4 + -32t + -16t2

Reorder the terms:
-4 + -32t + -16t2 = 4 + -4 + 32t + -32t + 16t2 + -16t2

Combine like terms: 4 + -4 = 0
-4 + -32t + -16t2 = 0 + 32t + -32t + 16t2 + -16t2
-4 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
-4 + -32t + -16t2 = 0 + 16t2 + -16t2
-4 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-4 + -32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(1 + 8t + 4t2) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(1 + 8t + 4t2)' equal to zero and attempt to solve:

Simplifying
1 + 8t + 4t2 = 0

Solving
1 + 8t + 4t2 = 0

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

Divide each side by '4'.
0.25 + 2t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 2t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 2t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 2t + t2 = 0 + -0.25
2t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
2t + t2 = -0.25

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = -0.25 + 1

Reorder the terms:
1 + 2t + t2 = -0.25 + 1

Combine like terms: -0.25 + 1 = 0.75
1 + 2t + t2 = 0.75

Factor a perfect square on the left side:
(t + 1)(t + 1) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(t + 1) equal to 0.866025404 and -0.866025404.

Subproblem 1
t + 1 = 0.866025404

Simplifying
t + 1 = 0.866025404

Reorder the terms:
1 + t = 0.866025404

Solving
1 + t = 0.866025404

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 0.866025404 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0.866025404 + -1
t = 0.866025404 + -1

Combine like terms: 0.866025404 + -1 = -0.133974596
t = -0.133974596

Simplifying
t = -0.133974596

Subproblem 2
t + 1 = -0.866025404

Simplifying
t + 1 = -0.866025404

Reorder the terms:
1 + t = -0.866025404

Solving
1 + t = -0.866025404

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -0.866025404 + -1

Combine like terms: 1 + -1 = 0
0 + t = -0.866025404 + -1
t = -0.866025404 + -1

Combine like terms: -0.866025404 + -1 = -1.866025404
t = -1.866025404

Simplifying
t = -1.866025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.133974596, -1.866025404}
Solution
t = {-0.133974596, -1.866025404}