4096t=-16t^2+4096

Solution for 4096t=-16t^2+4096 equation:

Simplifying
4096t = -16t2 + 4096

Reorder the terms:
4096t = 4096 + -16t2

Solving
4096t = 4096 + -16t2

Solving for variable 't'.

Reorder the terms:
-4096 + 4096t + 16t2 = 4096 + -16t2 + -4096 + 16t2

Reorder the terms:
-4096 + 4096t + 16t2 = 4096 + -4096 + -16t2 + 16t2

Combine like terms: 4096 + -4096 = 0
-4096 + 4096t + 16t2 = 0 + -16t2 + 16t2
-4096 + 4096t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-4096 + 4096t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-256 + 256t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-256 + 256t + t2)' equal to zero and attempt to solve:

Simplifying
-256 + 256t + t2 = 0

Solving
-256 + 256t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + 256t + 256 + t2 = 0 + 256

Reorder the terms:
-256 + 256 + 256t + t2 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + 256t + t2 = 0 + 256
256t + t2 = 0 + 256

Combine like terms: 0 + 256 = 256
256t + t2 = 256

The t term is 256t.  Take half its coefficient (128).
Square it (16384) and add it to both sides.

Add '16384' to each side of the equation.
256t + 16384 + t2 = 256 + 16384

Reorder the terms:
16384 + 256t + t2 = 256 + 16384

Combine like terms: 256 + 16384 = 16640
16384 + 256t + t2 = 16640

Factor a perfect square on the left side:
(t + 128)(t + 128) = 16640

Calculate the square root of the right side: 128.996123973

Break this problem into two subproblems by setting 
(t + 128) equal to 128.996123973 and -128.996123973.

Subproblem 1
t + 128 = 128.996123973

Simplifying
t + 128 = 128.996123973

Reorder the terms:
128 + t = 128.996123973

Solving
128 + t = 128.996123973

Solving for variable 't'.

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

Add '-128' to each side of the equation.
128 + -128 + t = 128.996123973 + -128

Combine like terms: 128 + -128 = 0
0 + t = 128.996123973 + -128
t = 128.996123973 + -128

Combine like terms: 128.996123973 + -128 = 0.996123973
t = 0.996123973

Simplifying
t = 0.996123973

Subproblem 2
t + 128 = -128.996123973

Simplifying
t + 128 = -128.996123973

Reorder the terms:
128 + t = -128.996123973

Solving
128 + t = -128.996123973

Solving for variable 't'.

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

Add '-128' to each side of the equation.
128 + -128 + t = -128.996123973 + -128

Combine like terms: 128 + -128 = 0
0 + t = -128.996123973 + -128
t = -128.996123973 + -128

Combine like terms: -128.996123973 + -128 = -256.996123973
t = -256.996123973

Simplifying
t = -256.996123973

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.996123973, -256.996123973}
Solution
t = {0.996123973, -256.996123973}