3k^2+18k-9=0

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

Simplifying
3k2 + 18k + -9 = 0

Reorder the terms:
-9 + 18k + 3k2 = 0

Solving
-9 + 18k + 3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 6k + k2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + 6k + k2)' equal to zero and attempt to solve:

Simplifying
-3 + 6k + k2 = 0

Solving
-3 + 6k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6k + 3 + k2 = 0 + 3

Reorder the terms:
-3 + 3 + 6k + k2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6k + k2 = 0 + 3
6k + k2 = 0 + 3

Combine like terms: 0 + 3 = 3
6k + k2 = 3

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

Add '9' to each side of the equation.
6k + 9 + k2 = 3 + 9

Reorder the terms:
9 + 6k + k2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6k + k2 = 12

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

Calculate the square root of the right side: 3.464101615

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

Subproblem 1
k + 3 = 3.464101615

Simplifying
k + 3 = 3.464101615

Reorder the terms:
3 + k = 3.464101615

Solving
3 + k = 3.464101615

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = 3.464101615 + -3

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

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

Simplifying
k = 0.464101615

Subproblem 2
k + 3 = -3.464101615

Simplifying
k + 3 = -3.464101615

Reorder the terms:
3 + k = -3.464101615

Solving
3 + k = -3.464101615

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = -3.464101615 + -3

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

Combine like terms: -3.464101615 + -3 = -6.464101615
k = -6.464101615

Simplifying
k = -6.464101615

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