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

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

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

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

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

Multiply (6 + n) * (2 + 7n)
(6(2 + 7n) + n(2 + 7n)) = 0
((2 * 6 + 7n * 6) + n(2 + 7n)) = 0
((12 + 42n) + n(2 + 7n)) = 0
(12 + 42n + (2 * n + 7n * n)) = 0
(12 + 42n + (2n + 7n2)) = 0

Combine like terms: 42n + 2n = 44n
(12 + 44n + 7n2) = 0

Solving
12 + 44n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(6 + n)(2 + 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 '(2 + 7n)' equal to zero and attempt to solve:

Simplifying
2 + 7n = 0

Solving
2 + 7n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7n = 0 + -2

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

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

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

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