(7k+1)(k+6)=0

Solution for (7k+1)(k+6)=0 equation:

Simplifying
(7k + 1)(k + 6) = 0

Reorder the terms:
(1 + 7k)(k + 6) = 0

Reorder the terms:
(1 + 7k)(6 + k) = 0

Multiply (1 + 7k) * (6 + k)
(1(6 + k) + 7k * (6 + k)) = 0
((6 * 1 + k * 1) + 7k * (6 + k)) = 0
((6 + 1k) + 7k * (6 + k)) = 0
(6 + 1k + (6 * 7k + k * 7k)) = 0
(6 + 1k + (42k + 7k2)) = 0

Combine like terms: 1k + 42k = 43k
(6 + 43k + 7k2) = 0

Solving
6 + 43k + 7k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(6 + k)(1 + 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 '(1 + 7k)' equal to zero and attempt to solve:

Simplifying
1 + 7k = 0

Solving
1 + 7k = 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 + 7k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7k = 0 + -1
7k = 0 + -1

Combine like terms: 0 + -1 = -1
7k = -1

Divide each side by '7'.
k = -0.1428571429

Simplifying
k = -0.1428571429
Solution
k = {-6, -0.1428571429}