10=48t-16t^2

Solution for 10=48t-16t^2 equation:

Simplifying
10 = 48t + -16t2

Solving
10 = 48t + -16t2

Solving for variable 't'.

Reorder the terms:
10 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
10 + -48t + 16t2 = 0 + -16t2 + 16t2
10 + -48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
10 + -48t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -24t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -24t + 8t2)' equal to zero and attempt to solve:

Simplifying
5 + -24t + 8t2 = 0

Solving
5 + -24t + 8t2 = 0

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

Divide each side by '8'.
0.625 + -3t + t2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -3t + -0.625 + t2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -3t + t2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -3t + t2 = 0 + -0.625
-3t + t2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-3t + t2 = -0.625

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -0.625 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -0.625 + 2.25

Combine like terms: -0.625 + 2.25 = 1.625
2.25 + -3t + t2 = 1.625

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 1.625

Calculate the square root of the right side: 1.274754878

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.274754878 and -1.274754878.

Subproblem 1
t + -1.5 = 1.274754878

Simplifying
t + -1.5 = 1.274754878

Reorder the terms:
-1.5 + t = 1.274754878

Solving
-1.5 + t = 1.274754878

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 1.274754878 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.274754878 + 1.5
t = 1.274754878 + 1.5

Combine like terms: 1.274754878 + 1.5 = 2.774754878
t = 2.774754878

Simplifying
t = 2.774754878

Subproblem 2
t + -1.5 = -1.274754878

Simplifying
t + -1.5 = -1.274754878

Reorder the terms:
-1.5 + t = -1.274754878

Solving
-1.5 + t = -1.274754878

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -1.274754878 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.274754878 + 1.5
t = -1.274754878 + 1.5

Combine like terms: -1.274754878 + 1.5 = 0.225245122
t = 0.225245122

Simplifying
t = 0.225245122

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.774754878, 0.225245122}
Solution
t = {2.774754878, 0.225245122}