0=-16t^2+112t-6

Solution for 0=-16t^2+112t-6 equation:

Simplifying
0 = -16t2 + 112t + -6

Reorder the terms:
0 = -6 + 112t + -16t2

Solving
0 = -6 + 112t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 6 = 6
6 + -112t + 16t2 = -6 + 112t + -16t2 + 6 + -112t + 16t2

Reorder the terms:
6 + -112t + 16t2 = -6 + 6 + 112t + -112t + -16t2 + 16t2

Combine like terms: -6 + 6 = 0
6 + -112t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2
6 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2

Combine like terms: 112t + -112t = 0
6 + -112t + 16t2 = 0 + -16t2 + 16t2
6 + -112t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
6 + -112t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -56t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -56t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + -56t + 8t2 = 0

Solving
3 + -56t + 8t2 = 0

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

Divide each side by '8'.
0.375 + -7t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -7t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -7t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -7t + t2 = 0 + -0.375
-7t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-7t + t2 = -0.375

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = -0.375 + 12.25

Reorder the terms:
12.25 + -7t + t2 = -0.375 + 12.25

Combine like terms: -0.375 + 12.25 = 11.875
12.25 + -7t + t2 = 11.875

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 11.875

Calculate the square root of the right side: 3.446012188

Break this problem into two subproblems by setting 
(t + -3.5) equal to 3.446012188 and -3.446012188.

Subproblem 1
t + -3.5 = 3.446012188

Simplifying
t + -3.5 = 3.446012188

Reorder the terms:
-3.5 + t = 3.446012188

Solving
-3.5 + t = 3.446012188

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 3.446012188 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 3.446012188 + 3.5
t = 3.446012188 + 3.5

Combine like terms: 3.446012188 + 3.5 = 6.946012188
t = 6.946012188

Simplifying
t = 6.946012188

Subproblem 2
t + -3.5 = -3.446012188

Simplifying
t + -3.5 = -3.446012188

Reorder the terms:
-3.5 + t = -3.446012188

Solving
-3.5 + t = -3.446012188

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -3.446012188 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -3.446012188 + 3.5
t = -3.446012188 + 3.5

Combine like terms: -3.446012188 + 3.5 = 0.053987812
t = 0.053987812

Simplifying
t = 0.053987812

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.946012188, 0.053987812}
Solution
t = {6.946012188, 0.053987812}