(n+6)(7n+6)=0

Solution for (n+6)(7n+6)=0 equation:

Simplifying
(n + 6)(7n + 6) = 0

Reorder the terms:
(6 + n)(7n + 6) = 0

Reorder the terms:
(6 + n)(6 + 7n) = 0

Multiply (6 + n) * (6 + 7n)
(6(6 + 7n) + n(6 + 7n)) = 0
((6 * 6 + 7n * 6) + n(6 + 7n)) = 0
((36 + 42n) + n(6 + 7n)) = 0
(36 + 42n + (6 * n + 7n * n)) = 0
(36 + 42n + (6n + 7n2)) = 0

Combine like terms: 42n + 6n = 48n
(36 + 48n + 7n2) = 0

Solving
36 + 48n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(6 + n)(6 + 7n) = 0

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

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

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

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

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

Simplifying
6 + 7n = 0

Solving
6 + 7n = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7n = 0 + -6
7n = 0 + -6

Combine like terms: 0 + -6 = -6
7n = -6

Divide each side by '7'.
n = -0.8571428571

Simplifying
n = -0.8571428571
Solution
n = {-6, -0.8571428571}