(5n+6)(n+7)=0

Solution for (5n+6)(n+7)=0 equation:

Simplifying
(5n + 6)(n + 7) = 0

Reorder the terms:
(6 + 5n)(n + 7) = 0

Reorder the terms:
(6 + 5n)(7 + n) = 0

Multiply (6 + 5n) * (7 + n)
(6(7 + n) + 5n * (7 + n)) = 0
((7 * 6 + n * 6) + 5n * (7 + n)) = 0
((42 + 6n) + 5n * (7 + n)) = 0
(42 + 6n + (7 * 5n + n * 5n)) = 0
(42 + 6n + (35n + 5n2)) = 0

Combine like terms: 6n + 35n = 41n
(42 + 41n + 5n2) = 0

Solving
42 + 41n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(7 + n)(6 + 5n) = 0

Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

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

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

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

Simplifying
n = -7
Subproblem 2
Set the factor '(6 + 5n)' equal to zero and attempt to solve:

Simplifying
6 + 5n = 0

Solving
6 + 5n = 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 + 5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5n = 0 + -6
5n = 0 + -6

Combine like terms: 0 + -6 = -6
5n = -6

Divide each side by '5'.
n = -1.2

Simplifying
n = -1.2
Solution
n = {-7, -1.2}