0=-3t^2+27t+5

Solution for 0=-3t^2+27t+5 equation:

Simplifying
0 = -3t2 + 27t + 5

Reorder the terms:
0 = 5 + 27t + -3t2

Solving
0 = 5 + 27t + -3t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + -27t + 3t2 = 5 + 27t + -3t2 + -5 + -27t + 3t2

Reorder the terms:
-5 + -27t + 3t2 = 5 + -5 + 27t + -27t + -3t2 + 3t2

Combine like terms: 5 + -5 = 0
-5 + -27t + 3t2 = 0 + 27t + -27t + -3t2 + 3t2
-5 + -27t + 3t2 = 27t + -27t + -3t2 + 3t2

Combine like terms: 27t + -27t = 0
-5 + -27t + 3t2 = 0 + -3t2 + 3t2
-5 + -27t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
-5 + -27t + 3t2 = 0

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

Divide each side by '3'.
-1.666666667 + -9t + t2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -9t + 1.666666667 + t2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -9t + t2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -9t + t2 = 0 + 1.666666667
-9t + t2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-9t + t2 = 1.666666667

The t term is -9t.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9t + 20.25 + t2 = 1.666666667 + 20.25

Reorder the terms:
20.25 + -9t + t2 = 1.666666667 + 20.25

Combine like terms: 1.666666667 + 20.25 = 21.916666667
20.25 + -9t + t2 = 21.916666667

Factor a perfect square on the left side:
(t + -4.5)(t + -4.5) = 21.916666667

Calculate the square root of the right side: 4.681523968

Break this problem into two subproblems by setting 
(t + -4.5) equal to 4.681523968 and -4.681523968.

Subproblem 1
t + -4.5 = 4.681523968

Simplifying
t + -4.5 = 4.681523968

Reorder the terms:
-4.5 + t = 4.681523968

Solving
-4.5 + t = 4.681523968

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = 4.681523968 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = 4.681523968 + 4.5
t = 4.681523968 + 4.5

Combine like terms: 4.681523968 + 4.5 = 9.181523968
t = 9.181523968

Simplifying
t = 9.181523968

Subproblem 2
t + -4.5 = -4.681523968

Simplifying
t + -4.5 = -4.681523968

Reorder the terms:
-4.5 + t = -4.681523968

Solving
-4.5 + t = -4.681523968

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = -4.681523968 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = -4.681523968 + 4.5
t = -4.681523968 + 4.5

Combine like terms: -4.681523968 + 4.5 = -0.181523968
t = -0.181523968

Simplifying
t = -0.181523968

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.181523968, -0.181523968}