6K(K+2)=K-3

Solution for 6K(K+2)=K-3 equation:

Simplifying
6K(K + 2) = K + -3

Reorder the terms:
6K(2 + K) = K + -3
(2 * 6K + K * 6K) = K + -3
(12K + 6K2) = K + -3

Reorder the terms:
12K + 6K2 = -3 + K

Solving
12K + 6K2 = -3 + K

Solving for variable 'K'.

Reorder the terms:
3 + 12K + -1K + 6K2 = -3 + K + 3 + -1K

Combine like terms: 12K + -1K = 11K
3 + 11K + 6K2 = -3 + K + 3 + -1K

Reorder the terms:
3 + 11K + 6K2 = -3 + 3 + K + -1K

Combine like terms: -3 + 3 = 0
3 + 11K + 6K2 = 0 + K + -1K
3 + 11K + 6K2 = K + -1K

Combine like terms: K + -1K = 0
3 + 11K + 6K2 = 0

Factor a trinomial.
(3 + 2K)(1 + 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 '(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
Solution
K = {-1.5, -0.3333333333}