16t^2+32t+9=0

Solution for 16t^2+32t+9=0 equation:

Simplifying
16t2 + 32t + 9 = 0

Reorder the terms:
9 + 32t + 16t2 = 0

Solving
9 + 32t + 16t2 = 0

Solving for variable 't'.

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

Divide each side by '16'.
0.5625 + 2t + t2 = 0

Move the constant term to the right:

Add '-0.5625' to each side of the equation.
0.5625 + 2t + -0.5625 + t2 = 0 + -0.5625

Reorder the terms:
0.5625 + -0.5625 + 2t + t2 = 0 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + 2t + t2 = 0 + -0.5625
2t + t2 = 0 + -0.5625

Combine like terms: 0 + -0.5625 = -0.5625
2t + t2 = -0.5625

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 = -0.5625 + 1

Reorder the terms:
1 + 2t + t2 = -0.5625 + 1

Combine like terms: -0.5625 + 1 = 0.4375
1 + 2t + t2 = 0.4375

Factor a perfect square on the left side:
(t + 1)(t + 1) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(t + 1) equal to 0.661437828 and -0.661437828.

Subproblem 1
t + 1 = 0.661437828

Simplifying
t + 1 = 0.661437828

Reorder the terms:
1 + t = 0.661437828

Solving
1 + t = 0.661437828

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 = 0.661437828 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0.661437828 + -1
t = 0.661437828 + -1

Combine like terms: 0.661437828 + -1 = -0.338562172
t = -0.338562172

Simplifying
t = -0.338562172

Subproblem 2
t + 1 = -0.661437828

Simplifying
t + 1 = -0.661437828

Reorder the terms:
1 + t = -0.661437828

Solving
1 + t = -0.661437828

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 = -0.661437828 + -1

Combine like terms: 1 + -1 = 0
0 + t = -0.661437828 + -1
t = -0.661437828 + -1

Combine like terms: -0.661437828 + -1 = -1.661437828
t = -1.661437828

Simplifying
t = -1.661437828

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.338562172, -1.661437828}