2k(k-1)=2(k+2)

Solution for 2k(k-1)=2(k+2) equation:

Simplifying
2k(k + -1) = 2(k + 2)

Reorder the terms:
2k(-1 + k) = 2(k + 2)
(-1 * 2k + k * 2k) = 2(k + 2)
(-2k + 2k2) = 2(k + 2)

Reorder the terms:
-2k + 2k2 = 2(2 + k)
-2k + 2k2 = (2 * 2 + k * 2)
-2k + 2k2 = (4 + 2k)

Solving
-2k + 2k2 = 4 + 2k

Solving for variable 'k'.

Reorder the terms:
-4 + -2k + -2k + 2k2 = 4 + 2k + -4 + -2k

Combine like terms: -2k + -2k = -4k
-4 + -4k + 2k2 = 4 + 2k + -4 + -2k

Reorder the terms:
-4 + -4k + 2k2 = 4 + -4 + 2k + -2k

Combine like terms: 4 + -4 = 0
-4 + -4k + 2k2 = 0 + 2k + -2k
-4 + -4k + 2k2 = 2k + -2k

Combine like terms: 2k + -2k = 0
-4 + -4k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -2k + k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -2k + k2)' equal to zero and attempt to solve:

Simplifying
-2 + -2k + k2 = 0

Solving
-2 + -2k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2k + 2 + k2 = 0 + 2

Reorder the terms:
-2 + 2 + -2k + k2 = 0 + 2

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

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

The k term is -2k.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2k + 1 + k2 = 2 + 1

Reorder the terms:
1 + -2k + k2 = 2 + 1

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

Factor a perfect square on the left side:
(k + -1)(k + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(k + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
k + -1 = 1.732050808

Simplifying
k + -1 = 1.732050808

Reorder the terms:
-1 + k = 1.732050808

Solving
-1 + k = 1.732050808

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + k = 1.732050808 + 1
k = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
k = 2.732050808

Simplifying
k = 2.732050808

Subproblem 2
k + -1 = -1.732050808

Simplifying
k + -1 = -1.732050808

Reorder the terms:
-1 + k = -1.732050808

Solving
-1 + k = -1.732050808

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + k = -1.732050808 + 1
k = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
k = -0.732050808

Simplifying
k = -0.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.732050808, -0.732050808}
Solution
k = {2.732050808, -0.732050808}