0=10+128t-16t^2

Solution for 0=10+128t-16t^2 equation:

Simplifying
0 = 10 + 128t + -16t2

Solving
0 = 10 + 128t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -10 = -10
-10 + -128t + 16t2 = 10 + 128t + -16t2 + -10 + -128t + 16t2

Reorder the terms:
-10 + -128t + 16t2 = 10 + -10 + 128t + -128t + -16t2 + 16t2

Combine like terms: 10 + -10 = 0
-10 + -128t + 16t2 = 0 + 128t + -128t + -16t2 + 16t2
-10 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2

Combine like terms: 128t + -128t = 0
-10 + -128t + 16t2 = 0 + -16t2 + 16t2
-10 + -128t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-10 + -128t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -64t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -64t + 8t2)' equal to zero and attempt to solve:

Simplifying
-5 + -64t + 8t2 = 0

Solving
-5 + -64t + 8t2 = 0

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

Divide each side by '8'.
-0.625 + -8t + t2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -8t + 0.625 + t2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -8t + t2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -8t + t2 = 0 + 0.625
-8t + t2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-8t + t2 = 0.625

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = 0.625 + 16

Reorder the terms:
16 + -8t + t2 = 0.625 + 16

Combine like terms: 0.625 + 16 = 16.625
16 + -8t + t2 = 16.625

Factor a perfect square on the left side:
(t + -4)(t + -4) = 16.625

Calculate the square root of the right side: 4.077376608

Break this problem into two subproblems by setting 
(t + -4) equal to 4.077376608 and -4.077376608.

Subproblem 1
t + -4 = 4.077376608

Simplifying
t + -4 = 4.077376608

Reorder the terms:
-4 + t = 4.077376608

Solving
-4 + t = 4.077376608

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = 4.077376608 + 4

Combine like terms: -4 + 4 = 0
0 + t = 4.077376608 + 4
t = 4.077376608 + 4

Combine like terms: 4.077376608 + 4 = 8.077376608
t = 8.077376608

Simplifying
t = 8.077376608

Subproblem 2
t + -4 = -4.077376608

Simplifying
t + -4 = -4.077376608

Reorder the terms:
-4 + t = -4.077376608

Solving
-4 + t = -4.077376608

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = -4.077376608 + 4

Combine like terms: -4 + 4 = 0
0 + t = -4.077376608 + 4
t = -4.077376608 + 4

Combine like terms: -4.077376608 + 4 = -0.077376608
t = -0.077376608

Simplifying
t = -0.077376608

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.077376608, -0.077376608}
Solution
t = {8.077376608, -0.077376608}