(5n+7)(n+5)=23

Solution for (5n+7)(n+5)=23 equation:

Simplifying
(5n + 7)(n + 5) = 23

Reorder the terms:
(7 + 5n)(n + 5) = 23

Reorder the terms:
(7 + 5n)(5 + n) = 23

Multiply (7 + 5n) * (5 + n)
(7(5 + n) + 5n * (5 + n)) = 23
((5 * 7 + n * 7) + 5n * (5 + n)) = 23
((35 + 7n) + 5n * (5 + n)) = 23
(35 + 7n + (5 * 5n + n * 5n)) = 23
(35 + 7n + (25n + 5n2)) = 23

Combine like terms: 7n + 25n = 32n
(35 + 32n + 5n2) = 23

Solving
35 + 32n + 5n2 = 23

Solving for variable 'n'.

Reorder the terms:
35 + -23 + 32n + 5n2 = 23 + -23

Combine like terms: 35 + -23 = 12
12 + 32n + 5n2 = 23 + -23

Combine like terms: 23 + -23 = 0
12 + 32n + 5n2 = 0

Factor a trinomial.
(6 + n)(2 + 5n) = 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 + 5n)' equal to zero and attempt to solve:

Simplifying
2 + 5n = 0

Solving
2 + 5n = 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 + 5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5n = 0 + -2
5n = 0 + -2

Combine like terms: 0 + -2 = -2
5n = -2

Divide each side by '5'.
n = -0.4

Simplifying
n = -0.4
Solution
n = {-6, -0.4}