8=32t-16t^2

Solution for 8=32t-16t^2 equation:

Simplifying
8 = 32t + -16t2

Solving
8 = 32t + -16t2

Solving for variable 't'.

Reorder the terms:
8 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
8 + -32t + 16t2 = 0 + -16t2 + 16t2
8 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
8 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + -4t + 2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(1 + -4t + 2t2)' equal to zero and attempt to solve:

Simplifying
1 + -4t + 2t2 = 0

Solving
1 + -4t + 2t2 = 0

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

Divide each side by '2'.
0.5 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -2t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -2t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -2t + t2 = 0 + -0.5
-2t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-2t + t2 = -0.5

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -0.5 + 1

Reorder the terms:
1 + -2t + t2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + -2t + t2 = 0.5

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(t + -1) equal to 0.707106781 and -0.707106781.

Subproblem 1
t + -1 = 0.707106781

Simplifying
t + -1 = 0.707106781

Reorder the terms:
-1 + t = 0.707106781

Solving
-1 + t = 0.707106781

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.707106781 + 1
t = 0.707106781 + 1

Combine like terms: 0.707106781 + 1 = 1.707106781
t = 1.707106781

Simplifying
t = 1.707106781

Subproblem 2
t + -1 = -0.707106781

Simplifying
t + -1 = -0.707106781

Reorder the terms:
-1 + t = -0.707106781

Solving
-1 + t = -0.707106781

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.707106781 + 1
t = -0.707106781 + 1

Combine like terms: -0.707106781 + 1 = 0.292893219
t = 0.292893219

Simplifying
t = 0.292893219

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.707106781, 0.292893219}
Solution
t = {1.707106781, 0.292893219}