12=6+21t-16t^2

Solution for 12=6+21t-16t^2 equation:

Simplifying
12 = 6 + 21t + -16t2

Solving
12 = 6 + 21t + -16t2

Solving for variable 't'.

Combine like terms: 12 + -6 = 6
6 + -21t + 16t2 = 6 + 21t + -16t2 + -6 + -21t + 16t2

Reorder the terms:
6 + -21t + 16t2 = 6 + -6 + 21t + -21t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
6 + -21t + 16t2 = 0 + 21t + -21t + -16t2 + 16t2
6 + -21t + 16t2 = 21t + -21t + -16t2 + 16t2

Combine like terms: 21t + -21t = 0
6 + -21t + 16t2 = 0 + -16t2 + 16t2
6 + -21t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
6 + -21t + 16t2 = 0

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

Divide each side by '16'.
0.375 + -1.3125t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -1.3125t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -1.3125t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -1.3125t + t2 = 0 + -0.375
-1.3125t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-1.3125t + t2 = -0.375

The t term is -1.3125t.  Take half its coefficient (-0.65625).
Square it (0.4306640625) and add it to both sides.

Add '0.4306640625' to each side of the equation.
-1.3125t + 0.4306640625 + t2 = -0.375 + 0.4306640625

Reorder the terms:
0.4306640625 + -1.3125t + t2 = -0.375 + 0.4306640625

Combine like terms: -0.375 + 0.4306640625 = 0.0556640625
0.4306640625 + -1.3125t + t2 = 0.0556640625

Factor a perfect square on the left side:
(t + -0.65625)(t + -0.65625) = 0.0556640625

Calculate the square root of the right side: 0.235932326

Break this problem into two subproblems by setting 
(t + -0.65625) equal to 0.235932326 and -0.235932326.

Subproblem 1
t + -0.65625 = 0.235932326

Simplifying
t + -0.65625 = 0.235932326

Reorder the terms:
-0.65625 + t = 0.235932326

Solving
-0.65625 + t = 0.235932326

Solving for variable 't'.

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

Add '0.65625' to each side of the equation.
-0.65625 + 0.65625 + t = 0.235932326 + 0.65625

Combine like terms: -0.65625 + 0.65625 = 0.00000
0.00000 + t = 0.235932326 + 0.65625
t = 0.235932326 + 0.65625

Combine like terms: 0.235932326 + 0.65625 = 0.892182326
t = 0.892182326

Simplifying
t = 0.892182326

Subproblem 2
t + -0.65625 = -0.235932326

Simplifying
t + -0.65625 = -0.235932326

Reorder the terms:
-0.65625 + t = -0.235932326

Solving
-0.65625 + t = -0.235932326

Solving for variable 't'.

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

Add '0.65625' to each side of the equation.
-0.65625 + 0.65625 + t = -0.235932326 + 0.65625

Combine like terms: -0.65625 + 0.65625 = 0.00000
0.00000 + t = -0.235932326 + 0.65625
t = -0.235932326 + 0.65625

Combine like terms: -0.235932326 + 0.65625 = 0.420317674
t = 0.420317674

Simplifying
t = 0.420317674

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.892182326, 0.420317674}