64(t)=-16t^2+48t+64

Solution for 64(t)=-16t^2+48t+64 equation:

Simplifying
64(t) = -16t2 + 48t + 64

Reorder the terms:
64t = 64 + 48t + -16t2

Solving
64t = 64 + 48t + -16t2

Solving for variable 't'.

Reorder the terms:
-64 + 64t + -48t + 16t2 = 64 + 48t + -16t2 + -64 + -48t + 16t2

Combine like terms: 64t + -48t = 16t
-64 + 16t + 16t2 = 64 + 48t + -16t2 + -64 + -48t + 16t2

Reorder the terms:
-64 + 16t + 16t2 = 64 + -64 + 48t + -48t + -16t2 + 16t2

Combine like terms: 64 + -64 = 0
-64 + 16t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2
-64 + 16t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
-64 + 16t + 16t2 = 0 + -16t2 + 16t2
-64 + 16t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-64 + 16t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-4 + t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-4 + t + t2)' equal to zero and attempt to solve:

Simplifying
-4 + t + t2 = 0

Solving
-4 + t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + t + t2 = 0 + 4
t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
t + t2 = 4

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
t + 0.25 + t2 = 4 + 0.25

Reorder the terms:
0.25 + t + t2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + t + t2 = 4.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(t + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
t + 0.5 = 2.061552813

Simplifying
t + 0.5 = 2.061552813

Reorder the terms:
0.5 + t = 2.061552813

Solving
0.5 + t = 2.061552813

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 2.061552813 + -0.5
t = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
t = 1.561552813

Simplifying
t = 1.561552813

Subproblem 2
t + 0.5 = -2.061552813

Simplifying
t + 0.5 = -2.061552813

Reorder the terms:
0.5 + t = -2.061552813

Solving
0.5 + t = -2.061552813

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -2.061552813 + -0.5
t = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
t = -2.561552813

Simplifying
t = -2.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.561552813, -2.561552813}
Solution
t = {1.561552813, -2.561552813}