28=6+40t-16t^2

Solution for 28=6+40t-16t^2 equation:

Simplifying
28 = 6 + 40t + -16t2

Solving
28 = 6 + 40t + -16t2

Solving for variable 't'.

Combine like terms: 28 + -6 = 22
22 + -40t + 16t2 = 6 + 40t + -16t2 + -6 + -40t + 16t2

Reorder the terms:
22 + -40t + 16t2 = 6 + -6 + 40t + -40t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
22 + -40t + 16t2 = 0 + 40t + -40t + -16t2 + 16t2
22 + -40t + 16t2 = 40t + -40t + -16t2 + 16t2

Combine like terms: 40t + -40t = 0
22 + -40t + 16t2 = 0 + -16t2 + 16t2
22 + -40t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
22 + -40t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -20t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + -20t + 8t2)' equal to zero and attempt to solve:

Simplifying
11 + -20t + 8t2 = 0

Solving
11 + -20t + 8t2 = 0

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

Divide each side by '8'.
1.375 + -2.5t + t2 = 0

Move the constant term to the right:

Add '-1.375' to each side of the equation.
1.375 + -2.5t + -1.375 + t2 = 0 + -1.375

Reorder the terms:
1.375 + -1.375 + -2.5t + t2 = 0 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + -2.5t + t2 = 0 + -1.375
-2.5t + t2 = 0 + -1.375

Combine like terms: 0 + -1.375 = -1.375
-2.5t + t2 = -1.375

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = -1.375 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = -1.375 + 1.5625

Combine like terms: -1.375 + 1.5625 = 0.1875
1.5625 + -2.5t + t2 = 0.1875

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 0.1875

Calculate the square root of the right side: 0.433012702

Break this problem into two subproblems by setting 
(t + -1.25) equal to 0.433012702 and -0.433012702.

Subproblem 1
t + -1.25 = 0.433012702

Simplifying
t + -1.25 = 0.433012702

Reorder the terms:
-1.25 + t = 0.433012702

Solving
-1.25 + t = 0.433012702

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = 0.433012702 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = 0.433012702 + 1.25
t = 0.433012702 + 1.25

Combine like terms: 0.433012702 + 1.25 = 1.683012702
t = 1.683012702

Simplifying
t = 1.683012702

Subproblem 2
t + -1.25 = -0.433012702

Simplifying
t + -1.25 = -0.433012702

Reorder the terms:
-1.25 + t = -0.433012702

Solving
-1.25 + t = -0.433012702

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = -0.433012702 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = -0.433012702 + 1.25
t = -0.433012702 + 1.25

Combine like terms: -0.433012702 + 1.25 = 0.816987298
t = 0.816987298

Simplifying
t = 0.816987298

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.683012702, 0.816987298}
Solution
t = {1.683012702, 0.816987298}