6=-3t^2+36t

Solution for 6=-3t^2+36t equation:

Simplifying
6 = -3t2 + 36t

Reorder the terms:
6 = 36t + -3t2

Solving
6 = 36t + -3t2

Solving for variable 't'.

Reorder the terms:
6 + -36t + 3t2 = 36t + -36t + -3t2 + 3t2

Combine like terms: 36t + -36t = 0
6 + -36t + 3t2 = 0 + -3t2 + 3t2
6 + -36t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
6 + -36t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -12t + t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -12t + t2)' equal to zero and attempt to solve:

Simplifying
2 + -12t + t2 = 0

Solving
2 + -12t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -12t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + -12t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -12t + t2 = 0 + -2
-12t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-12t + t2 = -2

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 = -2 + 36

Reorder the terms:
36 + -12t + t2 = -2 + 36

Combine like terms: -2 + 36 = 34
36 + -12t + t2 = 34

Factor a perfect square on the left side:
(t + -6)(t + -6) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(t + -6) equal to 5.830951895 and -5.830951895.

Subproblem 1
t + -6 = 5.830951895

Simplifying
t + -6 = 5.830951895

Reorder the terms:
-6 + t = 5.830951895

Solving
-6 + t = 5.830951895

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 = 5.830951895 + 6

Combine like terms: -6 + 6 = 0
0 + t = 5.830951895 + 6
t = 5.830951895 + 6

Combine like terms: 5.830951895 + 6 = 11.830951895
t = 11.830951895

Simplifying
t = 11.830951895

Subproblem 2
t + -6 = -5.830951895

Simplifying
t + -6 = -5.830951895

Reorder the terms:
-6 + t = -5.830951895

Solving
-6 + t = -5.830951895

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 = -5.830951895 + 6

Combine like terms: -6 + 6 = 0
0 + t = -5.830951895 + 6
t = -5.830951895 + 6

Combine like terms: -5.830951895 + 6 = 0.169048105
t = 0.169048105

Simplifying
t = 0.169048105

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.830951895, 0.169048105}
Solution
t = {11.830951895, 0.169048105}