0=64-3t-5t^2

Solution for 0=64-3t-5t^2 equation:

Simplifying
0 = 64 + -3t + -5t2

Solving
0 = 64 + -3t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -64 = -64
-64 + 3t + 5t2 = 64 + -3t + -5t2 + -64 + 3t + 5t2

Reorder the terms:
-64 + 3t + 5t2 = 64 + -64 + -3t + 3t + -5t2 + 5t2

Combine like terms: 64 + -64 = 0
-64 + 3t + 5t2 = 0 + -3t + 3t + -5t2 + 5t2
-64 + 3t + 5t2 = -3t + 3t + -5t2 + 5t2

Combine like terms: -3t + 3t = 0
-64 + 3t + 5t2 = 0 + -5t2 + 5t2
-64 + 3t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-64 + 3t + 5t2 = 0

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

Divide each side by '5'.
-12.8 + 0.6t + t2 = 0

Move the constant term to the right:

Add '12.8' to each side of the equation.
-12.8 + 0.6t + 12.8 + t2 = 0 + 12.8

Reorder the terms:
-12.8 + 12.8 + 0.6t + t2 = 0 + 12.8

Combine like terms: -12.8 + 12.8 = 0.0
0.0 + 0.6t + t2 = 0 + 12.8
0.6t + t2 = 0 + 12.8

Combine like terms: 0 + 12.8 = 12.8
0.6t + t2 = 12.8

The t term is 0.6t.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6t + 0.09 + t2 = 12.8 + 0.09

Reorder the terms:
0.09 + 0.6t + t2 = 12.8 + 0.09

Combine like terms: 12.8 + 0.09 = 12.89
0.09 + 0.6t + t2 = 12.89

Factor a perfect square on the left side:
(t + 0.3)(t + 0.3) = 12.89

Calculate the square root of the right side: 3.590264614

Break this problem into two subproblems by setting 
(t + 0.3) equal to 3.590264614 and -3.590264614.

Subproblem 1
t + 0.3 = 3.590264614

Simplifying
t + 0.3 = 3.590264614

Reorder the terms:
0.3 + t = 3.590264614

Solving
0.3 + t = 3.590264614

Solving for variable 't'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + t = 3.590264614 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + t = 3.590264614 + -0.3
t = 3.590264614 + -0.3

Combine like terms: 3.590264614 + -0.3 = 3.290264614
t = 3.290264614

Simplifying
t = 3.290264614

Subproblem 2
t + 0.3 = -3.590264614

Simplifying
t + 0.3 = -3.590264614

Reorder the terms:
0.3 + t = -3.590264614

Solving
0.3 + t = -3.590264614

Solving for variable 't'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + t = -3.590264614 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + t = -3.590264614 + -0.3
t = -3.590264614 + -0.3

Combine like terms: -3.590264614 + -0.3 = -3.890264614
t = -3.890264614

Simplifying
t = -3.890264614

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.290264614, -3.890264614}