0=-16t^2+46t-6

Solution for 0=-16t^2+46t-6 equation:

Simplifying
0 = -16t2 + 46t + -6

Reorder the terms:
0 = -6 + 46t + -16t2

Solving
0 = -6 + 46t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 6 = 6
6 + -46t + 16t2 = -6 + 46t + -16t2 + 6 + -46t + 16t2

Reorder the terms:
6 + -46t + 16t2 = -6 + 6 + 46t + -46t + -16t2 + 16t2

Combine like terms: -6 + 6 = 0
6 + -46t + 16t2 = 0 + 46t + -46t + -16t2 + 16t2
6 + -46t + 16t2 = 46t + -46t + -16t2 + 16t2

Combine like terms: 46t + -46t = 0
6 + -46t + 16t2 = 0 + -16t2 + 16t2
6 + -46t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
6 + -46t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -23t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -23t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + -23t + 8t2 = 0

Solving
3 + -23t + 8t2 = 0

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

Divide each side by '8'.
0.375 + -2.875t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -2.875t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -2.875t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -2.875t + t2 = 0 + -0.375
-2.875t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-2.875t + t2 = -0.375

The t term is -2.875t.  Take half its coefficient (-1.4375).
Square it (2.06640625) and add it to both sides.

Add '2.06640625' to each side of the equation.
-2.875t + 2.06640625 + t2 = -0.375 + 2.06640625

Reorder the terms:
2.06640625 + -2.875t + t2 = -0.375 + 2.06640625

Combine like terms: -0.375 + 2.06640625 = 1.69140625
2.06640625 + -2.875t + t2 = 1.69140625

Factor a perfect square on the left side:
(t + -1.4375)(t + -1.4375) = 1.69140625

Calculate the square root of the right side: 1.300540753

Break this problem into two subproblems by setting 
(t + -1.4375) equal to 1.300540753 and -1.300540753.

Subproblem 1
t + -1.4375 = 1.300540753

Simplifying
t + -1.4375 = 1.300540753

Reorder the terms:
-1.4375 + t = 1.300540753

Solving
-1.4375 + t = 1.300540753

Solving for variable 't'.

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

Add '1.4375' to each side of the equation.
-1.4375 + 1.4375 + t = 1.300540753 + 1.4375

Combine like terms: -1.4375 + 1.4375 = 0.0000
0.0000 + t = 1.300540753 + 1.4375
t = 1.300540753 + 1.4375

Combine like terms: 1.300540753 + 1.4375 = 2.738040753
t = 2.738040753

Simplifying
t = 2.738040753

Subproblem 2
t + -1.4375 = -1.300540753

Simplifying
t + -1.4375 = -1.300540753

Reorder the terms:
-1.4375 + t = -1.300540753

Solving
-1.4375 + t = -1.300540753

Solving for variable 't'.

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

Add '1.4375' to each side of the equation.
-1.4375 + 1.4375 + t = -1.300540753 + 1.4375

Combine like terms: -1.4375 + 1.4375 = 0.0000
0.0000 + t = -1.300540753 + 1.4375
t = -1.300540753 + 1.4375

Combine like terms: -1.300540753 + 1.4375 = 0.136959247
t = 0.136959247

Simplifying
t = 0.136959247

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.738040753, 0.136959247}
Solution
t = {2.738040753, 0.136959247}