3+3(k+3)=k(k-2)+9

Solution for 3+3(k+3)=k(k-2)+9 equation:

Simplifying
3 + 3(k + 3) = k(k + -2) + 9

Reorder the terms:
3 + 3(3 + k) = k(k + -2) + 9
3 + (3 * 3 + k * 3) = k(k + -2) + 9
3 + (9 + 3k) = k(k + -2) + 9

Combine like terms: 3 + 9 = 12
12 + 3k = k(k + -2) + 9

Reorder the terms:
12 + 3k = k(-2 + k) + 9
12 + 3k = (-2 * k + k * k) + 9
12 + 3k = (-2k + k2) + 9

Reorder the terms:
12 + 3k = 9 + -2k + k2

Solving
12 + 3k = 9 + -2k + k2

Solving for variable 'k'.

Reorder the terms:
12 + -9 + 3k + 2k + -1k2 = 9 + -2k + k2 + -9 + 2k + -1k2

Combine like terms: 12 + -9 = 3
3 + 3k + 2k + -1k2 = 9 + -2k + k2 + -9 + 2k + -1k2

Combine like terms: 3k + 2k = 5k
3 + 5k + -1k2 = 9 + -2k + k2 + -9 + 2k + -1k2

Reorder the terms:
3 + 5k + -1k2 = 9 + -9 + -2k + 2k + k2 + -1k2

Combine like terms: 9 + -9 = 0
3 + 5k + -1k2 = 0 + -2k + 2k + k2 + -1k2
3 + 5k + -1k2 = -2k + 2k + k2 + -1k2

Combine like terms: -2k + 2k = 0
3 + 5k + -1k2 = 0 + k2 + -1k2
3 + 5k + -1k2 = k2 + -1k2

Combine like terms: k2 + -1k2 = 0
3 + 5k + -1k2 = 0

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

Divide each side by '-1'.
-3 + -5k + k2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -5k + 3 + k2 = 0 + 3

Reorder the terms:
-3 + 3 + -5k + k2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5k + k2 = 0 + 3
-5k + k2 = 0 + 3

Combine like terms: 0 + 3 = 3
-5k + k2 = 3

The k term is -5k.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5k + 6.25 + k2 = 3 + 6.25

Reorder the terms:
6.25 + -5k + k2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + -5k + k2 = 9.25

Factor a perfect square on the left side:
(k + -2.5)(k + -2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(k + -2.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
k + -2.5 = 3.041381265

Simplifying
k + -2.5 = 3.041381265

Reorder the terms:
-2.5 + k = 3.041381265

Solving
-2.5 + k = 3.041381265

Solving for variable 'k'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + k = 3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + k = 3.041381265 + 2.5
k = 3.041381265 + 2.5

Combine like terms: 3.041381265 + 2.5 = 5.541381265
k = 5.541381265

Simplifying
k = 5.541381265

Subproblem 2
k + -2.5 = -3.041381265

Simplifying
k + -2.5 = -3.041381265

Reorder the terms:
-2.5 + k = -3.041381265

Solving
-2.5 + k = -3.041381265

Solving for variable 'k'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + k = -3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + k = -3.041381265 + 2.5
k = -3.041381265 + 2.5

Combine like terms: -3.041381265 + 2.5 = -0.541381265
k = -0.541381265

Simplifying
k = -0.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {5.541381265, -0.541381265}