6=16t^2+24t+1

Solution for 6=16t^2+24t+1 equation:

Simplifying
6 = 16t2 + 24t + 1

Reorder the terms:
6 = 1 + 24t + 16t2

Solving
6 = 1 + 24t + 16t2

Solving for variable 't'.

Combine like terms: 6 + -1 = 5
5 + -24t + -16t2 = 1 + 24t + 16t2 + -1 + -24t + -16t2

Reorder the terms:
5 + -24t + -16t2 = 1 + -1 + 24t + -24t + 16t2 + -16t2

Combine like terms: 1 + -1 = 0
5 + -24t + -16t2 = 0 + 24t + -24t + 16t2 + -16t2
5 + -24t + -16t2 = 24t + -24t + 16t2 + -16t2

Combine like terms: 24t + -24t = 0
5 + -24t + -16t2 = 0 + 16t2 + -16t2
5 + -24t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
5 + -24t + -16t2 = 0

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

Divide each side by '-16'.
-0.3125 + 1.5t + t2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + 1.5t + 0.3125 + t2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + 1.5t + t2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + 1.5t + t2 = 0 + 0.3125
1.5t + t2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
1.5t + t2 = 0.3125

The t term is 1.5t.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5t + 0.5625 + t2 = 0.3125 + 0.5625

Reorder the terms:
0.5625 + 1.5t + t2 = 0.3125 + 0.5625

Combine like terms: 0.3125 + 0.5625 = 0.875
0.5625 + 1.5t + t2 = 0.875

Factor a perfect square on the left side:
(t + 0.75)(t + 0.75) = 0.875

Calculate the square root of the right side: 0.935414347

Break this problem into two subproblems by setting 
(t + 0.75) equal to 0.935414347 and -0.935414347.

Subproblem 1
t + 0.75 = 0.935414347

Simplifying
t + 0.75 = 0.935414347

Reorder the terms:
0.75 + t = 0.935414347

Solving
0.75 + t = 0.935414347

Solving for variable 't'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + t = 0.935414347 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + t = 0.935414347 + -0.75
t = 0.935414347 + -0.75

Combine like terms: 0.935414347 + -0.75 = 0.185414347
t = 0.185414347

Simplifying
t = 0.185414347

Subproblem 2
t + 0.75 = -0.935414347

Simplifying
t + 0.75 = -0.935414347

Reorder the terms:
0.75 + t = -0.935414347

Solving
0.75 + t = -0.935414347

Solving for variable 't'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + t = -0.935414347 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + t = -0.935414347 + -0.75
t = -0.935414347 + -0.75

Combine like terms: -0.935414347 + -0.75 = -1.685414347
t = -1.685414347

Simplifying
t = -1.685414347

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.185414347, -1.685414347}