9+6*t^2-18*t=0

Solution for 9+6*t^2-18*t=0 equation:

Simplifying
9 + 6t2 + -18t = 0

Reorder the terms:
9 + -18t + 6t2 = 0

Solving
9 + -18t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -6t + 2t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -6t + 2t2)' equal to zero and attempt to solve:

Simplifying
3 + -6t + 2t2 = 0

Solving
3 + -6t + 2t2 = 0

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

Divide each side by '2'.
1.5 + -3t + t2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -3t + -1.5 + t2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -3t + t2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -3t + t2 = 0 + -1.5
-3t + t2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-3t + t2 = -1.5

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -1.5 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -1.5 + 2.25

Combine like terms: -1.5 + 2.25 = 0.75
2.25 + -3t + t2 = 0.75

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(t + -1.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
t + -1.5 = 0.866025404

Simplifying
t + -1.5 = 0.866025404

Reorder the terms:
-1.5 + t = 0.866025404

Solving
-1.5 + t = 0.866025404

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 0.866025404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 0.866025404 + 1.5
t = 0.866025404 + 1.5

Combine like terms: 0.866025404 + 1.5 = 2.366025404
t = 2.366025404

Simplifying
t = 2.366025404

Subproblem 2
t + -1.5 = -0.866025404

Simplifying
t + -1.5 = -0.866025404

Reorder the terms:
-1.5 + t = -0.866025404

Solving
-1.5 + t = -0.866025404

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -0.866025404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -0.866025404 + 1.5
t = -0.866025404 + 1.5

Combine like terms: -0.866025404 + 1.5 = 0.633974596
t = 0.633974596

Simplifying
t = 0.633974596

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.366025404, 0.633974596}
Solution
t = {2.366025404, 0.633974596}