14=6+23t-16t^2

Solution for 14=6+23t-16t^2 equation:

Simplifying
14 = 6 + 23t + -16t2

Solving
14 = 6 + 23t + -16t2

Solving for variable 't'.

Combine like terms: 14 + -6 = 8
8 + -23t + 16t2 = 6 + 23t + -16t2 + -6 + -23t + 16t2

Reorder the terms:
8 + -23t + 16t2 = 6 + -6 + 23t + -23t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
8 + -23t + 16t2 = 0 + 23t + -23t + -16t2 + 16t2
8 + -23t + 16t2 = 23t + -23t + -16t2 + 16t2

Combine like terms: 23t + -23t = 0
8 + -23t + 16t2 = 0 + -16t2 + 16t2
8 + -23t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
8 + -23t + 16t2 = 0

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

Divide each side by '16'.
0.5 + -1.4375t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.4375t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.4375t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.4375t + t2 = 0 + -0.5
-1.4375t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1.4375t + t2 = -0.5

The t term is -1.4375t.  Take half its coefficient (-0.71875).
Square it (0.5166015625) and add it to both sides.

Add '0.5166015625' to each side of the equation.
-1.4375t + 0.5166015625 + t2 = -0.5 + 0.5166015625

Reorder the terms:
0.5166015625 + -1.4375t + t2 = -0.5 + 0.5166015625

Combine like terms: -0.5 + 0.5166015625 = 0.0166015625
0.5166015625 + -1.4375t + t2 = 0.0166015625

Factor a perfect square on the left side:
(t + -0.71875)(t + -0.71875) = 0.0166015625

Calculate the square root of the right side: 0.128847051

Break this problem into two subproblems by setting 
(t + -0.71875) equal to 0.128847051 and -0.128847051.

Subproblem 1
t + -0.71875 = 0.128847051

Simplifying
t + -0.71875 = 0.128847051

Reorder the terms:
-0.71875 + t = 0.128847051

Solving
-0.71875 + t = 0.128847051

Solving for variable 't'.

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

Add '0.71875' to each side of the equation.
-0.71875 + 0.71875 + t = 0.128847051 + 0.71875

Combine like terms: -0.71875 + 0.71875 = 0.00000
0.00000 + t = 0.128847051 + 0.71875
t = 0.128847051 + 0.71875

Combine like terms: 0.128847051 + 0.71875 = 0.847597051
t = 0.847597051

Simplifying
t = 0.847597051

Subproblem 2
t + -0.71875 = -0.128847051

Simplifying
t + -0.71875 = -0.128847051

Reorder the terms:
-0.71875 + t = -0.128847051

Solving
-0.71875 + t = -0.128847051

Solving for variable 't'.

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

Add '0.71875' to each side of the equation.
-0.71875 + 0.71875 + t = -0.128847051 + 0.71875

Combine like terms: -0.71875 + 0.71875 = 0.00000
0.00000 + t = -0.128847051 + 0.71875
t = -0.128847051 + 0.71875

Combine like terms: -0.128847051 + 0.71875 = 0.589902949
t = 0.589902949

Simplifying
t = 0.589902949

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.847597051, 0.589902949}