2k(k-3)=-3

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

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

Reorder the terms:
2k(-3 + k) = -3
(-3 * 2k + k * 2k) = -3
(-6k + 2k2) = -3

Solving
-6k + 2k2 = -3

Solving for variable 'k'.

Reorder the terms:
3 + -6k + 2k2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + -6k + 2k2 = 0

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

Divide each side by '2'.
1.5 + -3k + k2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -3k + -1.5 + k2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -3k + k2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -3k + k2 = 0 + -1.5
-3k + k2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-3k + k2 = -1.5

The k term is -3k.  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.
-3k + 2.25 + k2 = -1.5 + 2.25

Reorder the terms:
2.25 + -3k + k2 = -1.5 + 2.25

Combine like terms: -1.5 + 2.25 = 0.75
2.25 + -3k + k2 = 0.75

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

Calculate the square root of the right side: 0.866025404

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

Subproblem 1
k + -1.5 = 0.866025404

Simplifying
k + -1.5 = 0.866025404

Reorder the terms:
-1.5 + k = 0.866025404

Solving
-1.5 + k = 0.866025404

Solving for variable 'k'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = 0.866025404 + 1.5

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

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

Simplifying
k = 2.366025404

Subproblem 2
k + -1.5 = -0.866025404

Simplifying
k + -1.5 = -0.866025404

Reorder the terms:
-1.5 + k = -0.866025404

Solving
-1.5 + k = -0.866025404

Solving for variable 'k'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = -0.866025404 + 1.5

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

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

Simplifying
k = 0.633974596

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