0=255-21t-16t^2

Solution for 0=255-21t-16t^2 equation:

Simplifying
0 = 255 + -21t + -16t2

Solving
0 = 255 + -21t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -255 = -255
-255 + 21t + 16t2 = 255 + -21t + -16t2 + -255 + 21t + 16t2

Reorder the terms:
-255 + 21t + 16t2 = 255 + -255 + -21t + 21t + -16t2 + 16t2

Combine like terms: 255 + -255 = 0
-255 + 21t + 16t2 = 0 + -21t + 21t + -16t2 + 16t2
-255 + 21t + 16t2 = -21t + 21t + -16t2 + 16t2

Combine like terms: -21t + 21t = 0
-255 + 21t + 16t2 = 0 + -16t2 + 16t2
-255 + 21t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-255 + 21t + 16t2 = 0

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

Divide each side by '16'.
-15.9375 + 1.3125t + t2 = 0

Move the constant term to the right:

Add '15.9375' to each side of the equation.
-15.9375 + 1.3125t + 15.9375 + t2 = 0 + 15.9375

Reorder the terms:
-15.9375 + 15.9375 + 1.3125t + t2 = 0 + 15.9375

Combine like terms: -15.9375 + 15.9375 = 0.0000
0.0000 + 1.3125t + t2 = 0 + 15.9375
1.3125t + t2 = 0 + 15.9375

Combine like terms: 0 + 15.9375 = 15.9375
1.3125t + t2 = 15.9375

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 = 15.9375 + 0.4306640625

Reorder the terms:
0.4306640625 + 1.3125t + t2 = 15.9375 + 0.4306640625

Combine like terms: 15.9375 + 0.4306640625 = 16.3681640625
0.4306640625 + 1.3125t + t2 = 16.3681640625

Factor a perfect square on the left side:
(t + 0.65625)(t + 0.65625) = 16.3681640625

Calculate the square root of the right side: 4.045758775

Break this problem into two subproblems by setting 
(t + 0.65625) equal to 4.045758775 and -4.045758775.

Subproblem 1
t + 0.65625 = 4.045758775

Simplifying
t + 0.65625 = 4.045758775

Reorder the terms:
0.65625 + t = 4.045758775

Solving
0.65625 + t = 4.045758775

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 = 4.045758775 + -0.65625

Combine like terms: 0.65625 + -0.65625 = 0.00000
0.00000 + t = 4.045758775 + -0.65625
t = 4.045758775 + -0.65625

Combine like terms: 4.045758775 + -0.65625 = 3.389508775
t = 3.389508775

Simplifying
t = 3.389508775

Subproblem 2
t + 0.65625 = -4.045758775

Simplifying
t + 0.65625 = -4.045758775

Reorder the terms:
0.65625 + t = -4.045758775

Solving
0.65625 + t = -4.045758775

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 = -4.045758775 + -0.65625

Combine like terms: 0.65625 + -0.65625 = 0.00000
0.00000 + t = -4.045758775 + -0.65625
t = -4.045758775 + -0.65625

Combine like terms: -4.045758775 + -0.65625 = -4.702008775
t = -4.702008775

Simplifying
t = -4.702008775

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.389508775, -4.702008775}