2=16t^2+24t+5

Solution for 2=16t^2+24t+5 equation:

Simplifying
2 = 16t2 + 24t + 5

Reorder the terms:
2 = 5 + 24t + 16t2

Solving
2 = 5 + 24t + 16t2

Solving for variable 't'.

Combine like terms: 2 + -5 = -3
-3 + -24t + -16t2 = 5 + 24t + 16t2 + -5 + -24t + -16t2

Reorder the terms:
-3 + -24t + -16t2 = 5 + -5 + 24t + -24t + 16t2 + -16t2

Combine like terms: 5 + -5 = 0
-3 + -24t + -16t2 = 0 + 24t + -24t + 16t2 + -16t2
-3 + -24t + -16t2 = 24t + -24t + 16t2 + -16t2

Combine like terms: 24t + -24t = 0
-3 + -24t + -16t2 = 0 + 16t2 + -16t2
-3 + -24t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-3 + -24t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 24t + 16t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 24t + 16t2)' equal to zero and attempt to solve:

Simplifying
3 + 24t + 16t2 = 0

Solving
3 + 24t + 16t2 = 0

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

Divide each side by '16'.
0.1875 + 1.5t + t2 = 0

Move the constant term to the right:

Add '-0.1875' to each side of the equation.
0.1875 + 1.5t + -0.1875 + t2 = 0 + -0.1875

Reorder the terms:
0.1875 + -0.1875 + 1.5t + t2 = 0 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + 1.5t + t2 = 0 + -0.1875
1.5t + t2 = 0 + -0.1875

Combine like terms: 0 + -0.1875 = -0.1875
1.5t + t2 = -0.1875

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 = -0.1875 + 0.5625

Reorder the terms:
0.5625 + 1.5t + t2 = -0.1875 + 0.5625

Combine like terms: -0.1875 + 0.5625 = 0.375
0.5625 + 1.5t + t2 = 0.375

Factor a perfect square on the left side:
(t + 0.75)(t + 0.75) = 0.375

Calculate the square root of the right side: 0.612372436

Break this problem into two subproblems by setting 
(t + 0.75) equal to 0.612372436 and -0.612372436.

Subproblem 1
t + 0.75 = 0.612372436

Simplifying
t + 0.75 = 0.612372436

Reorder the terms:
0.75 + t = 0.612372436

Solving
0.75 + t = 0.612372436

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 = 0.612372436 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + t = 0.612372436 + -0.75
t = 0.612372436 + -0.75

Combine like terms: 0.612372436 + -0.75 = -0.137627564
t = -0.137627564

Simplifying
t = -0.137627564

Subproblem 2
t + 0.75 = -0.612372436

Simplifying
t + 0.75 = -0.612372436

Reorder the terms:
0.75 + t = -0.612372436

Solving
0.75 + t = -0.612372436

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 = -0.612372436 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + t = -0.612372436 + -0.75
t = -0.612372436 + -0.75

Combine like terms: -0.612372436 + -0.75 = -1.362372436
t = -1.362372436

Simplifying
t = -1.362372436

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.137627564, -1.362372436}
Solution
t = {-0.137627564, -1.362372436}