6k(k+3)=k-12

Solution for 6k(k+3)=k-12 equation:

Simplifying
6k(k + 3) = k + -12

Reorder the terms:
6k(3 + k) = k + -12
(3 * 6k + k * 6k) = k + -12
(18k + 6k2) = k + -12

Reorder the terms:
18k + 6k2 = -12 + k

Solving
18k + 6k2 = -12 + k

Solving for variable 'k'.

Reorder the terms:
12 + 18k + -1k + 6k2 = -12 + k + 12 + -1k

Combine like terms: 18k + -1k = 17k
12 + 17k + 6k2 = -12 + k + 12 + -1k

Reorder the terms:
12 + 17k + 6k2 = -12 + 12 + k + -1k

Combine like terms: -12 + 12 = 0
12 + 17k + 6k2 = 0 + k + -1k
12 + 17k + 6k2 = k + -1k

Combine like terms: k + -1k = 0
12 + 17k + 6k2 = 0

Factor a trinomial.
(3 + 2k)(4 + 3k) = 0

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

Simplifying
3 + 2k = 0

Solving
3 + 2k = 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 + 2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2k = 0 + -3
2k = 0 + -3

Combine like terms: 0 + -3 = -3
2k = -3

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
Subproblem 2
Set the factor '(4 + 3k)' equal to zero and attempt to solve:

Simplifying
4 + 3k = 0

Solving
4 + 3k = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3k = 0 + -4
3k = 0 + -4

Combine like terms: 0 + -4 = -4
3k = -4

Divide each side by '3'.
k = -1.333333333

Simplifying
k = -1.333333333
Solution
k = {-1.5, -1.333333333}