3(2k-2)=6k(k-1)

Solution for 3(2k-2)=6k(k-1) equation:

Simplifying
3(2k + -2) = 6k(k + -1)

Reorder the terms:
3(-2 + 2k) = 6k(k + -1)
(-2 * 3 + 2k * 3) = 6k(k + -1)
(-6 + 6k) = 6k(k + -1)

Reorder the terms:
-6 + 6k = 6k(-1 + k)
-6 + 6k = (-1 * 6k + k * 6k)
-6 + 6k = (-6k + 6k2)

Solving
-6 + 6k = -6k + 6k2

Solving for variable 'k'.

Combine like terms: 6k + 6k = 12k
-6 + 12k + -6k2 = -6k + 6k2 + 6k + -6k2

Reorder the terms:
-6 + 12k + -6k2 = -6k + 6k + 6k2 + -6k2

Combine like terms: -6k + 6k = 0
-6 + 12k + -6k2 = 0 + 6k2 + -6k2
-6 + 12k + -6k2 = 6k2 + -6k2

Combine like terms: 6k2 + -6k2 = 0
-6 + 12k + -6k2 = 0

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

Factor a trinomial.
6((-1 + k)(1 + -1k)) = 0

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

Simplifying
-1 + k = 0

Solving
-1 + k = 0

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 = 0 + 1

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

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

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

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

Simplifying
k = 1
Solution
k = {1, 1}