0=3t^2-18t+6

Solution for 0=3t^2-18t+6 equation:

Simplifying
0 = 3t2 + -18t + 6

Reorder the terms:
0 = 6 + -18t + 3t2

Solving
0 = 6 + -18t + 3t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + 18t + -3t2 = 6 + -18t + 3t2 + -6 + 18t + -3t2

Reorder the terms:
-6 + 18t + -3t2 = 6 + -6 + -18t + 18t + 3t2 + -3t2

Combine like terms: 6 + -6 = 0
-6 + 18t + -3t2 = 0 + -18t + 18t + 3t2 + -3t2
-6 + 18t + -3t2 = -18t + 18t + 3t2 + -3t2

Combine like terms: -18t + 18t = 0
-6 + 18t + -3t2 = 0 + 3t2 + -3t2
-6 + 18t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-6 + 18t + -3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 6t + -1t2) = 0

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

Simplifying
-2 + 6t + -1t2 = 0

Solving
-2 + 6t + -1t2 = 0

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

Divide each side by '-1'.
2 + -6t + t2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -6t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + -6t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -6t + t2 = 0 + -2
-6t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-6t + t2 = -2

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 = -2 + 9

Reorder the terms:
9 + -6t + t2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6t + t2 = 7

Factor a perfect square on the left side:
(t + -3)(t + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + -3) equal to 2.645751311 and -2.645751311.

Subproblem 1
t + -3 = 2.645751311

Simplifying
t + -3 = 2.645751311

Reorder the terms:
-3 + t = 2.645751311

Solving
-3 + t = 2.645751311

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 = 2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + t = 2.645751311 + 3
t = 2.645751311 + 3

Combine like terms: 2.645751311 + 3 = 5.645751311
t = 5.645751311

Simplifying
t = 5.645751311

Subproblem 2
t + -3 = -2.645751311

Simplifying
t + -3 = -2.645751311

Reorder the terms:
-3 + t = -2.645751311

Solving
-3 + t = -2.645751311

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 = -2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + t = -2.645751311 + 3
t = -2.645751311 + 3

Combine like terms: -2.645751311 + 3 = 0.354248689
t = 0.354248689

Simplifying
t = 0.354248689

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.645751311, 0.354248689}
Solution
t = {5.645751311, 0.354248689}