(k+6)(3k+7)=0

Solution for (k+6)(3k+7)=0 equation:

Simplifying
(k + 6)(3k + 7) = 0

Reorder the terms:
(6 + k)(3k + 7) = 0

Reorder the terms:
(6 + k)(7 + 3k) = 0

Multiply (6 + k) * (7 + 3k)
(6(7 + 3k) + k(7 + 3k)) = 0
((7 * 6 + 3k * 6) + k(7 + 3k)) = 0
((42 + 18k) + k(7 + 3k)) = 0
(42 + 18k + (7 * k + 3k * k)) = 0
(42 + 18k + (7k + 3k2)) = 0

Combine like terms: 18k + 7k = 25k
(42 + 25k + 3k2) = 0

Solving
42 + 25k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(6 + k)(7 + 3k) = 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 '(7 + 3k)' equal to zero and attempt to solve:

Simplifying
7 + 3k = 0

Solving
7 + 3k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 3k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3k = 0 + -7
3k = 0 + -7

Combine like terms: 0 + -7 = -7
3k = -7

Divide each side by '3'.
k = -2.333333333

Simplifying
k = -2.333333333
Solution
k = {-6, -2.333333333}