20=-5t^2+60t

Solution for 20=-5t^2+60t equation:

Simplifying
20 = -5t2 + 60t

Reorder the terms:
20 = 60t + -5t2

Solving
20 = 60t + -5t2

Solving for variable 't'.

Reorder the terms:
20 + -60t + 5t2 = 60t + -60t + -5t2 + 5t2

Combine like terms: 60t + -60t = 0
20 + -60t + 5t2 = 0 + -5t2 + 5t2
20 + -60t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
20 + -60t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -12t + t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(4 + -12t + t2)' equal to zero and attempt to solve:

Simplifying
4 + -12t + t2 = 0

Solving
4 + -12t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -12t + -4 + t2 = 0 + -4

Reorder the terms:
4 + -4 + -12t + t2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -12t + t2 = 0 + -4
-12t + t2 = 0 + -4

Combine like terms: 0 + -4 = -4
-12t + t2 = -4

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = -4 + 36

Reorder the terms:
36 + -12t + t2 = -4 + 36

Combine like terms: -4 + 36 = 32
36 + -12t + t2 = 32

Factor a perfect square on the left side:
(t + -6)(t + -6) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(t + -6) equal to 5.656854249 and -5.656854249.

Subproblem 1
t + -6 = 5.656854249

Simplifying
t + -6 = 5.656854249

Reorder the terms:
-6 + t = 5.656854249

Solving
-6 + t = 5.656854249

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = 5.656854249 + 6

Combine like terms: -6 + 6 = 0
0 + t = 5.656854249 + 6
t = 5.656854249 + 6

Combine like terms: 5.656854249 + 6 = 11.656854249
t = 11.656854249

Simplifying
t = 11.656854249

Subproblem 2
t + -6 = -5.656854249

Simplifying
t + -6 = -5.656854249

Reorder the terms:
-6 + t = -5.656854249

Solving
-6 + t = -5.656854249

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = -5.656854249 + 6

Combine like terms: -6 + 6 = 0
0 + t = -5.656854249 + 6
t = -5.656854249 + 6

Combine like terms: -5.656854249 + 6 = 0.343145751
t = 0.343145751

Simplifying
t = 0.343145751

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.656854249, 0.343145751}
Solution
t = {11.656854249, 0.343145751}