=16t^2+126t+5

Solution for =16t^2+126t+5 equation:

Simplifying
0 = 16t2 + 126t + 5

Reorder the terms:
0 = 5 + 126t + 16t2

Solving
0 = 5 + 126t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + -126t + -16t2 = 5 + 126t + 16t2 + -5 + -126t + -16t2

Reorder the terms:
-5 + -126t + -16t2 = 5 + -5 + 126t + -126t + 16t2 + -16t2

Combine like terms: 5 + -5 = 0
-5 + -126t + -16t2 = 0 + 126t + -126t + 16t2 + -16t2
-5 + -126t + -16t2 = 126t + -126t + 16t2 + -16t2

Combine like terms: 126t + -126t = 0
-5 + -126t + -16t2 = 0 + 16t2 + -16t2
-5 + -126t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-5 + -126t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 126t + 16t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 126t + 16t2)' equal to zero and attempt to solve:

Simplifying
5 + 126t + 16t2 = 0

Solving
5 + 126t + 16t2 = 0

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

Divide each side by '16'.
0.3125 + 7.875t + t2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + 7.875t + -0.3125 + t2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + 7.875t + t2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + 7.875t + t2 = 0 + -0.3125
7.875t + t2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
7.875t + t2 = -0.3125

The t term is 7.875t.  Take half its coefficient (3.9375).
Square it (15.50390625) and add it to both sides.

Add '15.50390625' to each side of the equation.
7.875t + 15.50390625 + t2 = -0.3125 + 15.50390625

Reorder the terms:
15.50390625 + 7.875t + t2 = -0.3125 + 15.50390625

Combine like terms: -0.3125 + 15.50390625 = 15.19140625
15.50390625 + 7.875t + t2 = 15.19140625

Factor a perfect square on the left side:
(t + 3.9375)(t + 3.9375) = 15.19140625

Calculate the square root of the right side: 3.897615457

Break this problem into two subproblems by setting 
(t + 3.9375) equal to 3.897615457 and -3.897615457.

Subproblem 1
t + 3.9375 = 3.897615457

Simplifying
t + 3.9375 = 3.897615457

Reorder the terms:
3.9375 + t = 3.897615457

Solving
3.9375 + t = 3.897615457

Solving for variable 't'.

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

Add '-3.9375' to each side of the equation.
3.9375 + -3.9375 + t = 3.897615457 + -3.9375

Combine like terms: 3.9375 + -3.9375 = 0.0000
0.0000 + t = 3.897615457 + -3.9375
t = 3.897615457 + -3.9375

Combine like terms: 3.897615457 + -3.9375 = -0.039884543
t = -0.039884543

Simplifying
t = -0.039884543

Subproblem 2
t + 3.9375 = -3.897615457

Simplifying
t + 3.9375 = -3.897615457

Reorder the terms:
3.9375 + t = -3.897615457

Solving
3.9375 + t = -3.897615457

Solving for variable 't'.

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

Add '-3.9375' to each side of the equation.
3.9375 + -3.9375 + t = -3.897615457 + -3.9375

Combine like terms: 3.9375 + -3.9375 = 0.0000
0.0000 + t = -3.897615457 + -3.9375
t = -3.897615457 + -3.9375

Combine like terms: -3.897615457 + -3.9375 = -7.835115457
t = -7.835115457

Simplifying
t = -7.835115457

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.039884543, -7.835115457}
Solution
t = {-0.039884543, -7.835115457}