(16+96t-1+-16t)t=-16t^2+16t+96

Solution for (16+96t-1+-16t)t=-16t^2+16t+96 equation:

Simplifying
(16 + 96t + -1 + -16t) * t = -16t2 + 16t + 96

Reorder the terms:
(16 + -1 + 96t + -16t) * t = -16t2 + 16t + 96

Combine like terms: 16 + -1 = 15
(15 + 96t + -16t) * t = -16t2 + 16t + 96

Combine like terms: 96t + -16t = 80t
(15 + 80t) * t = -16t2 + 16t + 96

Reorder the terms for easier multiplication:
t(15 + 80t) = -16t2 + 16t + 96
(15 * t + 80t * t) = -16t2 + 16t + 96
(15t + 80t2) = -16t2 + 16t + 96

Reorder the terms:
15t + 80t2 = 96 + 16t + -16t2

Solving
15t + 80t2 = 96 + 16t + -16t2

Solving for variable 't'.

Reorder the terms:
-96 + 15t + -16t + 80t2 + 16t2 = 96 + 16t + -16t2 + -96 + -16t + 16t2

Combine like terms: 15t + -16t = -1t
-96 + -1t + 80t2 + 16t2 = 96 + 16t + -16t2 + -96 + -16t + 16t2

Combine like terms: 80t2 + 16t2 = 96t2
-96 + -1t + 96t2 = 96 + 16t + -16t2 + -96 + -16t + 16t2

Reorder the terms:
-96 + -1t + 96t2 = 96 + -96 + 16t + -16t + -16t2 + 16t2

Combine like terms: 96 + -96 = 0
-96 + -1t + 96t2 = 0 + 16t + -16t + -16t2 + 16t2
-96 + -1t + 96t2 = 16t + -16t + -16t2 + 16t2

Combine like terms: 16t + -16t = 0
-96 + -1t + 96t2 = 0 + -16t2 + 16t2
-96 + -1t + 96t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-96 + -1t + 96t2 = 0

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

Divide each side by '96'.
-1 + -0.01041666667t + t2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.01041666667t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.01041666667t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.01041666667t + t2 = 0 + 1
-0.01041666667t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.01041666667t + t2 = 1

The t term is -0.01041666667t.  Take half its coefficient (-0.005208333335).
Square it (0.00002712673613) and add it to both sides.

Add '0.00002712673613' to each side of the equation.
-0.01041666667t + 0.00002712673613 + t2 = 1 + 0.00002712673613

Reorder the terms:
0.00002712673613 + -0.01041666667t + t2 = 1 + 0.00002712673613

Combine like terms: 1 + 0.00002712673613 = 1.00002712673613
0.00002712673613 + -0.01041666667t + t2 = 1.00002712673613

Factor a perfect square on the left side:
(t + -0.005208333335)(t + -0.005208333335) = 1.00002712673613

Calculate the square root of the right side: 1.000013563

Break this problem into two subproblems by setting 
(t + -0.005208333335) equal to 1.000013563 and -1.000013563.

Subproblem 1
t + -0.005208333335 = 1.000013563

Simplifying
t + -0.005208333335 = 1.000013563

Reorder the terms:
-0.005208333335 + t = 1.000013563

Solving
-0.005208333335 + t = 1.000013563

Solving for variable 't'.

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

Add '0.005208333335' to each side of the equation.
-0.005208333335 + 0.005208333335 + t = 1.000013563 + 0.005208333335

Combine like terms: -0.005208333335 + 0.005208333335 = 0.000000000000
0.000000000000 + t = 1.000013563 + 0.005208333335
t = 1.000013563 + 0.005208333335

Combine like terms: 1.000013563 + 0.005208333335 = 1.005221896335
t = 1.005221896335

Simplifying
t = 1.005221896335

Subproblem 2
t + -0.005208333335 = -1.000013563

Simplifying
t + -0.005208333335 = -1.000013563

Reorder the terms:
-0.005208333335 + t = -1.000013563

Solving
-0.005208333335 + t = -1.000013563

Solving for variable 't'.

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

Add '0.005208333335' to each side of the equation.
-0.005208333335 + 0.005208333335 + t = -1.000013563 + 0.005208333335

Combine like terms: -0.005208333335 + 0.005208333335 = 0.000000000000
0.000000000000 + t = -1.000013563 + 0.005208333335
t = -1.000013563 + 0.005208333335

Combine like terms: -1.000013563 + 0.005208333335 = -0.994805229665
t = -0.994805229665

Simplifying
t = -0.994805229665

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.005221896335, -0.994805229665}