0=6+29t+16t^2

Solution for 0=6+29t+16t^2 equation:

Simplifying
0 = 6 + 29t + 16t2

Solving
0 = 6 + 29t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + -29t + -16t2 = 6 + 29t + 16t2 + -6 + -29t + -16t2

Reorder the terms:
-6 + -29t + -16t2 = 6 + -6 + 29t + -29t + 16t2 + -16t2

Combine like terms: 6 + -6 = 0
-6 + -29t + -16t2 = 0 + 29t + -29t + 16t2 + -16t2
-6 + -29t + -16t2 = 29t + -29t + 16t2 + -16t2

Combine like terms: 29t + -29t = 0
-6 + -29t + -16t2 = 0 + 16t2 + -16t2
-6 + -29t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-6 + -29t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 29t + 16t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 29t + 16t2)' equal to zero and attempt to solve:

Simplifying
6 + 29t + 16t2 = 0

Solving
6 + 29t + 16t2 = 0

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

Divide each side by '16'.
0.375 + 1.8125t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 1.8125t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 1.8125t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 1.8125t + t2 = 0 + -0.375
1.8125t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
1.8125t + t2 = -0.375

The t term is 1.8125t.  Take half its coefficient (0.90625).
Square it (0.8212890625) and add it to both sides.

Add '0.8212890625' to each side of the equation.
1.8125t + 0.8212890625 + t2 = -0.375 + 0.8212890625

Reorder the terms:
0.8212890625 + 1.8125t + t2 = -0.375 + 0.8212890625

Combine like terms: -0.375 + 0.8212890625 = 0.4462890625
0.8212890625 + 1.8125t + t2 = 0.4462890625

Factor a perfect square on the left side:
(t + 0.90625)(t + 0.90625) = 0.4462890625

Calculate the square root of the right side: 0.668048698

Break this problem into two subproblems by setting 
(t + 0.90625) equal to 0.668048698 and -0.668048698.

Subproblem 1
t + 0.90625 = 0.668048698

Simplifying
t + 0.90625 = 0.668048698

Reorder the terms:
0.90625 + t = 0.668048698

Solving
0.90625 + t = 0.668048698

Solving for variable 't'.

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

Add '-0.90625' to each side of the equation.
0.90625 + -0.90625 + t = 0.668048698 + -0.90625

Combine like terms: 0.90625 + -0.90625 = 0.00000
0.00000 + t = 0.668048698 + -0.90625
t = 0.668048698 + -0.90625

Combine like terms: 0.668048698 + -0.90625 = -0.238201302
t = -0.238201302

Simplifying
t = -0.238201302

Subproblem 2
t + 0.90625 = -0.668048698

Simplifying
t + 0.90625 = -0.668048698

Reorder the terms:
0.90625 + t = -0.668048698

Solving
0.90625 + t = -0.668048698

Solving for variable 't'.

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

Add '-0.90625' to each side of the equation.
0.90625 + -0.90625 + t = -0.668048698 + -0.90625

Combine like terms: 0.90625 + -0.90625 = 0.00000
0.00000 + t = -0.668048698 + -0.90625
t = -0.668048698 + -0.90625

Combine like terms: -0.668048698 + -0.90625 = -1.574298698
t = -1.574298698

Simplifying
t = -1.574298698

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.238201302, -1.574298698}
Solution
t = {-0.238201302, -1.574298698}