2(3k+1)(k-6)=0

Solution for 2(3k+1)(k-6)=0 equation:

Simplifying
2(3k + 1)(k + -6) = 0

Reorder the terms:
2(1 + 3k)(k + -6) = 0

Reorder the terms:
2(1 + 3k)(-6 + k) = 0

Multiply (1 + 3k) * (-6 + k)
2(1(-6 + k) + 3k * (-6 + k)) = 0
2((-6 * 1 + k * 1) + 3k * (-6 + k)) = 0
2((-6 + 1k) + 3k * (-6 + k)) = 0
2(-6 + 1k + (-6 * 3k + k * 3k)) = 0
2(-6 + 1k + (-18k + 3k2)) = 0

Combine like terms: 1k + -18k = -17k
2(-6 + -17k + 3k2) = 0
(-6 * 2 + -17k * 2 + 3k2 * 2) = 0
(-12 + -34k + 6k2) = 0

Solving
-12 + -34k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -17k + 3k2) = 0

Factor a trinomial.
2((-1 + -3k)(6 + -1k)) = 0

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

Simplifying
-1 + -3k = 0

Solving
-1 + -3k = 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 + -3k = 0 + 1

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

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

Divide each side by '-3'.
k = -0.3333333333

Simplifying
k = -0.3333333333
Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1k = 0 + -6
-1k = 0 + -6

Combine like terms: 0 + -6 = -6
-1k = -6

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {-0.3333333333, 6}