(7n+5)(n+3)=0

Solution for (7n+5)(n+3)=0 equation:

Simplifying
(7n + 5)(n + 3) = 0

Reorder the terms:
(5 + 7n)(n + 3) = 0

Reorder the terms:
(5 + 7n)(3 + n) = 0

Multiply (5 + 7n) * (3 + n)
(5(3 + n) + 7n * (3 + n)) = 0
((3 * 5 + n * 5) + 7n * (3 + n)) = 0
((15 + 5n) + 7n * (3 + n)) = 0
(15 + 5n + (3 * 7n + n * 7n)) = 0
(15 + 5n + (21n + 7n2)) = 0

Combine like terms: 5n + 21n = 26n
(15 + 26n + 7n2) = 0

Solving
15 + 26n + 7n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(5 + 7n)' equal to zero and attempt to solve:

Simplifying
5 + 7n = 0

Solving
5 + 7n = 0

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

Add '-5' to each side of the equation.
5 + -5 + 7n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7n = 0 + -5
7n = 0 + -5

Combine like terms: 0 + -5 = -5
7n = -5

Divide each side by '7'.
n = -0.7142857143

Simplifying
n = -0.7142857143
Solution
n = {-3, -0.7142857143}