(n+3)x(2n+5)=

Solution for (n+3)x(2n+5)= equation:

Simplifying
(n + 3) * x(2n + 5) = 0

Reorder the terms:
(3 + n) * x(2n + 5) = 0

Reorder the terms:
(3 + n) * x(5 + 2n) = 0

Reorder the terms for easier multiplication:
x(3 + n)(5 + 2n) = 0

Multiply (3 + n) * (5 + 2n)
x(3(5 + 2n) + n(5 + 2n)) = 0
x((5 * 3 + 2n * 3) + n(5 + 2n)) = 0
x((15 + 6n) + n(5 + 2n)) = 0
x(15 + 6n + (5 * n + 2n * n)) = 0
x(15 + 6n + (5n + 2n2)) = 0

Combine like terms: 6n + 5n = 11n
x(15 + 11n + 2n2) = 0
(15 * x + 11n * x + 2n2 * x) = 0

Reorder the terms:
(11nx + 2n2x + 15x) = 0
(11nx + 2n2x + 15x) = 0

Solving
11nx + 2n2x + 15x = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(11n + 2n2 + 15) = 0

Factor a trinomial.
x((2n + 5)(n + 3)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2n + 5)' equal to zero and attempt to solve:

Simplifying
2n + 5 = 0

Reorder the terms:
5 + 2n = 0

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

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

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

Divide each side by '2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 3
Set the factor '(n + 3)' equal to zero and attempt to solve:

Simplifying
n + 3 = 0

Reorder the terms:
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
Solution
n = {-2.5, -3}