(7k+2)(k+6)=0

Solution for (7k+2)(k+6)=0 equation:

Simplifying
(7k + 2)(k + 6) = 0

Reorder the terms:
(2 + 7k)(k + 6) = 0

Reorder the terms:
(2 + 7k)(6 + k) = 0

Multiply (2 + 7k) * (6 + k)
(2(6 + k) + 7k * (6 + k)) = 0
((6 * 2 + k * 2) + 7k * (6 + k)) = 0
((12 + 2k) + 7k * (6 + k)) = 0
(12 + 2k + (6 * 7k + k * 7k)) = 0
(12 + 2k + (42k + 7k2)) = 0

Combine like terms: 2k + 42k = 44k
(12 + 44k + 7k2) = 0

Solving
12 + 44k + 7k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(6 + k)(2 + 7k) = 0

Subproblem 1
Set the factor '(6 + k)' equal to zero and attempt to solve:

Simplifying
6 + k = 0

Solving
6 + k = 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 + k = 0 + -6

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

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

Simplifying
k = -6
Subproblem 2
Set the factor '(2 + 7k)' equal to zero and attempt to solve:

Simplifying
2 + 7k = 0

Solving
2 + 7k = 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 + 7k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7k = 0 + -2
7k = 0 + -2

Combine like terms: 0 + -2 = -2
7k = -2

Divide each side by '7'.
k = -0.2857142857

Simplifying
k = -0.2857142857
Solution
k = {-6, -0.2857142857}