30=60t-5t^2

Solution for 30=60t-5t^2 equation:

Simplifying
30 = 60t + -5t2

Solving
30 = 60t + -5t2

Solving for variable 't'.

Reorder the terms:
30 + -60t + 5t2 = 60t + -60t + -5t2 + 5t2

Combine like terms: 60t + -60t = 0
30 + -60t + 5t2 = 0 + -5t2 + 5t2
30 + -60t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
30 + -60t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -12t + t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + -12t + t2)' equal to zero and attempt to solve:

Simplifying
6 + -12t + t2 = 0

Solving
6 + -12t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -12t + -6 + t2 = 0 + -6

Reorder the terms:
6 + -6 + -12t + t2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -12t + t2 = 0 + -6
-12t + t2 = 0 + -6

Combine like terms: 0 + -6 = -6
-12t + t2 = -6

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 = -6 + 36

Reorder the terms:
36 + -12t + t2 = -6 + 36

Combine like terms: -6 + 36 = 30
36 + -12t + t2 = 30

Factor a perfect square on the left side:
(t + -6)(t + -6) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(t + -6) equal to 5.477225575 and -5.477225575.

Subproblem 1
t + -6 = 5.477225575

Simplifying
t + -6 = 5.477225575

Reorder the terms:
-6 + t = 5.477225575

Solving
-6 + t = 5.477225575

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 = 5.477225575 + 6

Combine like terms: -6 + 6 = 0
0 + t = 5.477225575 + 6
t = 5.477225575 + 6

Combine like terms: 5.477225575 + 6 = 11.477225575
t = 11.477225575

Simplifying
t = 11.477225575

Subproblem 2
t + -6 = -5.477225575

Simplifying
t + -6 = -5.477225575

Reorder the terms:
-6 + t = -5.477225575

Solving
-6 + t = -5.477225575

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 = -5.477225575 + 6

Combine like terms: -6 + 6 = 0
0 + t = -5.477225575 + 6
t = -5.477225575 + 6

Combine like terms: -5.477225575 + 6 = 0.522774425
t = 0.522774425

Simplifying
t = 0.522774425

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.477225575, 0.522774425}
Solution
t = {11.477225575, 0.522774425}