t-16t^2+32t-16=0

Solution for t-16t^2+32t-16=0 equation:

Simplifying
t + -16t2 + 32t + -16 = 0

Reorder the terms:
-16 + t + 32t + -16t2 = 0

Combine like terms: t + 32t = 33t
-16 + 33t + -16t2 = 0

Solving
-16 + 33t + -16t2 = 0

Solving for variable 't'.

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

Divide each side by '-16'.
1 + -2.0625t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.0625t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -2.0625t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.0625t + t2 = 0 + -1
-2.0625t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.0625t + t2 = -1

The t term is -2.0625t.  Take half its coefficient (-1.03125).
Square it (1.063476563) and add it to both sides.

Add '1.063476563' to each side of the equation.
-2.0625t + 1.063476563 + t2 = -1 + 1.063476563

Reorder the terms:
1.063476563 + -2.0625t + t2 = -1 + 1.063476563

Combine like terms: -1 + 1.063476563 = 0.063476563
1.063476563 + -2.0625t + t2 = 0.063476563

Factor a perfect square on the left side:
(t + -1.03125)(t + -1.03125) = 0.063476563

Calculate the square root of the right side: 0.251945556

Break this problem into two subproblems by setting 
(t + -1.03125) equal to 0.251945556 and -0.251945556.

Subproblem 1
t + -1.03125 = 0.251945556

Simplifying
t + -1.03125 = 0.251945556

Reorder the terms:
-1.03125 + t = 0.251945556

Solving
-1.03125 + t = 0.251945556

Solving for variable 't'.

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

Add '1.03125' to each side of the equation.
-1.03125 + 1.03125 + t = 0.251945556 + 1.03125

Combine like terms: -1.03125 + 1.03125 = 0.00000
0.00000 + t = 0.251945556 + 1.03125
t = 0.251945556 + 1.03125

Combine like terms: 0.251945556 + 1.03125 = 1.283195556
t = 1.283195556

Simplifying
t = 1.283195556

Subproblem 2
t + -1.03125 = -0.251945556

Simplifying
t + -1.03125 = -0.251945556

Reorder the terms:
-1.03125 + t = -0.251945556

Solving
-1.03125 + t = -0.251945556

Solving for variable 't'.

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

Add '1.03125' to each side of the equation.
-1.03125 + 1.03125 + t = -0.251945556 + 1.03125

Combine like terms: -1.03125 + 1.03125 = 0.00000
0.00000 + t = -0.251945556 + 1.03125
t = -0.251945556 + 1.03125

Combine like terms: -0.251945556 + 1.03125 = 0.779304444
t = 0.779304444

Simplifying
t = 0.779304444

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.283195556, 0.779304444}