6K(K+2)=5K-2

Solution for 6K(K+2)=5K-2 equation:

Simplifying
6K(K + 2) = 5K + -2

Reorder the terms:
6K(2 + K) = 5K + -2
(2 * 6K + K * 6K) = 5K + -2
(12K + 6K2) = 5K + -2

Reorder the terms:
12K + 6K2 = -2 + 5K

Solving
12K + 6K2 = -2 + 5K

Solving for variable 'K'.

Reorder the terms:
2 + 12K + -5K + 6K2 = -2 + 5K + 2 + -5K

Combine like terms: 12K + -5K = 7K
2 + 7K + 6K2 = -2 + 5K + 2 + -5K

Reorder the terms:
2 + 7K + 6K2 = -2 + 2 + 5K + -5K

Combine like terms: -2 + 2 = 0
2 + 7K + 6K2 = 0 + 5K + -5K
2 + 7K + 6K2 = 5K + -5K

Combine like terms: 5K + -5K = 0
2 + 7K + 6K2 = 0

Factor a trinomial.
(2 + 3K)(1 + 2K) = 0

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

Simplifying
2 + 3K = 0

Solving
2 + 3K = 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 + 3K = 0 + -2

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

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

Divide each side by '3'.
K = -0.6666666667

Simplifying
K = -0.6666666667
Subproblem 2
Set the factor '(1 + 2K)' equal to zero and attempt to solve:

Simplifying
1 + 2K = 0

Solving
1 + 2K = 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 + 2K = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2K = 0 + -1
2K = 0 + -1

Combine like terms: 0 + -1 = -1
2K = -1

Divide each side by '2'.
K = -0.5

Simplifying
K = -0.5
Solution
K = {-0.6666666667, -0.5}