-3t^2+18t+9=0

Solution for -3t^2+18t+9=0 equation:

Simplifying
-3t2 + 18t + 9 = 0

Reorder the terms:
9 + 18t + -3t2 = 0

Solving
9 + 18t + -3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 6t + -1t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 6t + -1t2)' equal to zero and attempt to solve:

Simplifying
3 + 6t + -1t2 = 0

Solving
3 + 6t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + -6t + t2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -6t + 3 + t2 = 0 + 3

Reorder the terms:
-3 + 3 + -6t + t2 = 0 + 3

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

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

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 3 + 9

Reorder the terms:
9 + -6t + t2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + -6t + t2 = 12

Factor a perfect square on the left side:
(t + -3)(t + -3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(t + -3) equal to 3.464101615 and -3.464101615.

Subproblem 1
t + -3 = 3.464101615

Simplifying
t + -3 = 3.464101615

Reorder the terms:
-3 + t = 3.464101615

Solving
-3 + t = 3.464101615

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + t = 3.464101615 + 3
t = 3.464101615 + 3

Combine like terms: 3.464101615 + 3 = 6.464101615
t = 6.464101615

Simplifying
t = 6.464101615

Subproblem 2
t + -3 = -3.464101615

Simplifying
t + -3 = -3.464101615

Reorder the terms:
-3 + t = -3.464101615

Solving
-3 + t = -3.464101615

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + t = -3.464101615 + 3
t = -3.464101615 + 3

Combine like terms: -3.464101615 + 3 = -0.464101615
t = -0.464101615

Simplifying
t = -0.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.464101615, -0.464101615}
Solution
t = {6.464101615, -0.464101615}