2k(k-1)=12

Solution for 2k(k-1)=12 equation:

Simplifying
2k(k + -1) = 12

Reorder the terms:
2k(-1 + k) = 12
(-1 * 2k + k * 2k) = 12
(-2k + 2k2) = 12

Solving
-2k + 2k2 = 12

Solving for variable 'k'.

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

Combine like terms: 12 + -12 = 0
-12 + -2k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1k + k2) = 0

Factor a trinomial.
2((-2 + -1k)(3 + -1k)) = 0

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

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1k = 0 + 2
-1k = 0 + 2

Combine like terms: 0 + 2 = 2
-1k = 2

Divide each side by '-1'.
k = -2

Simplifying
k = -2
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

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

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

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {-2, 3}