12k(k+2)=7k-6

Solution for 12k(k+2)=7k-6 equation:

Simplifying
12k(k + 2) = 7k + -6

Reorder the terms:
12k(2 + k) = 7k + -6
(2 * 12k + k * 12k) = 7k + -6
(24k + 12k2) = 7k + -6

Reorder the terms:
24k + 12k2 = -6 + 7k

Solving
24k + 12k2 = -6 + 7k

Solving for variable 'k'.

Reorder the terms:
6 + 24k + -7k + 12k2 = -6 + 7k + 6 + -7k

Combine like terms: 24k + -7k = 17k
6 + 17k + 12k2 = -6 + 7k + 6 + -7k

Reorder the terms:
6 + 17k + 12k2 = -6 + 6 + 7k + -7k

Combine like terms: -6 + 6 = 0
6 + 17k + 12k2 = 0 + 7k + -7k
6 + 17k + 12k2 = 7k + -7k

Combine like terms: 7k + -7k = 0
6 + 17k + 12k2 = 0

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

Subproblem 1
Set the factor '(3 + 4k)' equal to zero and attempt to solve:

Simplifying
3 + 4k = 0

Solving
3 + 4k = 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 + 4k = 0 + -3

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

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

Divide each side by '4'.
k = -0.75

Simplifying
k = -0.75
Subproblem 2
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
Solution
k = {-0.75, -0.6666666667}