0=16t^2+32t+2

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

Simplifying
0 = 16t2 + 32t + 2

Reorder the terms:
0 = 2 + 32t + 16t2

Solving
0 = 2 + 32t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -2 = -2
-2 + -32t + -16t2 = 2 + 32t + 16t2 + -2 + -32t + -16t2

Reorder the terms:
-2 + -32t + -16t2 = 2 + -2 + 32t + -32t + 16t2 + -16t2

Combine like terms: 2 + -2 = 0
-2 + -32t + -16t2 = 0 + 32t + -32t + 16t2 + -16t2
-2 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
-2 + -32t + -16t2 = 0 + 16t2 + -16t2
-2 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-2 + -32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 16t + 8t2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(1 + 16t + 8t2)' equal to zero and attempt to solve:

Simplifying
1 + 16t + 8t2 = 0

Solving
1 + 16t + 8t2 = 0

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

Divide each side by '8'.
0.125 + 2t + t2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 2t + -0.125 + t2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 2t + t2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 2t + t2 = 0 + -0.125
2t + t2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
2t + t2 = -0.125

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 = -0.125 + 1

Reorder the terms:
1 + 2t + t2 = -0.125 + 1

Combine like terms: -0.125 + 1 = 0.875
1 + 2t + t2 = 0.875

Factor a perfect square on the left side:
(t + 1)(t + 1) = 0.875

Calculate the square root of the right side: 0.935414347

Break this problem into two subproblems by setting 
(t + 1) equal to 0.935414347 and -0.935414347.

Subproblem 1
t + 1 = 0.935414347

Simplifying
t + 1 = 0.935414347

Reorder the terms:
1 + t = 0.935414347

Solving
1 + t = 0.935414347

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 = 0.935414347 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0.935414347 + -1
t = 0.935414347 + -1

Combine like terms: 0.935414347 + -1 = -0.064585653
t = -0.064585653

Simplifying
t = -0.064585653

Subproblem 2
t + 1 = -0.935414347

Simplifying
t + 1 = -0.935414347

Reorder the terms:
1 + t = -0.935414347

Solving
1 + t = -0.935414347

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 = -0.935414347 + -1

Combine like terms: 1 + -1 = 0
0 + t = -0.935414347 + -1
t = -0.935414347 + -1

Combine like terms: -0.935414347 + -1 = -1.935414347
t = -1.935414347

Simplifying
t = -1.935414347

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.064585653, -1.935414347}
Solution
t = {-0.064585653, -1.935414347}