0=-16t^2+64t-20

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Solution for 0=-16t^2+64t-20 equation: 


Simplifying
0 = -16t2 + 64t + -20

Reorder the terms:
0 = -20 + 64t + -16t2

Solving
0 = -20 + 64t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 20 = 20
20 + -64t + 16t2 = -20 + 64t + -16t2 + 20 + -64t + 16t2

Reorder the terms:
20 + -64t + 16t2 = -20 + 20 + 64t + -64t + -16t2 + 16t2

Combine like terms: -20 + 20 = 0
20 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2
20 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2

Combine like terms: 64t + -64t = 0
20 + -64t + 16t2 = 0 + -16t2 + 16t2
20 + -64t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
20 + -64t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -16t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -16t + 4t2)' equal to zero and attempt to solve:

Simplifying
5 + -16t + 4t2 = 0

Solving
5 + -16t + 4t2 = 0

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

Divide each side by '4'.
1.25 + -4t + t2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -4t + -1.25 + t2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -4t + t2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -4t + t2 = 0 + -1.25
-4t + t2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-4t + t2 = -1.25

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -1.25 + 4

Reorder the terms:
4 + -4t + t2 = -1.25 + 4

Combine like terms: -1.25 + 4 = 2.75
4 + -4t + t2 = 2.75

Factor a perfect square on the left side:
(t + -2)(t + -2) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(t + -2) equal to 1.658312395 and -1.658312395.


Subproblem 1
t + -2 = 1.658312395

Simplifying
t + -2 = 1.658312395

Reorder the terms:
-2 + t = 1.658312395

Solving
-2 + t = 1.658312395

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 1.658312395 + 2

Combine like terms: -2 + 2 = 0
0 + t = 1.658312395 + 2
t = 1.658312395 + 2

Combine like terms: 1.658312395 + 2 = 3.658312395
t = 3.658312395

Simplifying
t = 3.658312395


Subproblem 2
t + -2 = -1.658312395

Simplifying
t + -2 = -1.658312395

Reorder the terms:
-2 + t = -1.658312395

Solving
-2 + t = -1.658312395

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -1.658312395 + 2

Combine like terms: -2 + 2 = 0
0 + t = -1.658312395 + 2
t = -1.658312395 + 2

Combine like terms: -1.658312395 + 2 = 0.341687605
t = 0.341687605

Simplifying
t = 0.341687605


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.658312395, 0.341687605}
Solution
t = {3.658312395, 0.341687605}

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