6(k-1)(k+2)=0

Solution for 6(k-1)(k+2)=0 equation:

Simplifying
6(k + -1)(k + 2) = 0

Reorder the terms:
6(-1 + k)(k + 2) = 0

Reorder the terms:
6(-1 + k)(2 + k) = 0

Multiply (-1 + k) * (2 + k)
6(-1(2 + k) + k(2 + k)) = 0
6((2 * -1 + k * -1) + k(2 + k)) = 0
6((-2 + -1k) + k(2 + k)) = 0
6(-2 + -1k + (2 * k + k * k)) = 0
6(-2 + -1k + (2k + k2)) = 0

Combine like terms: -1k + 2k = 1k
6(-2 + 1k + k2) = 0
(-2 * 6 + 1k * 6 + k2 * 6) = 0
(-12 + 6k + 6k2) = 0

Solving
-12 + 6k + 6k2 = 0

Solving for variable 'k'.

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

Factor a trinomial.
6((-2 + -1k)(1 + -1k)) = 0

Ignore the factor 6.
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 '(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 = {-2, 1}