(n+4)x(n+9)=

Solution for (n+4)x(n+9)= equation:

Simplifying
(n + 4) * x(n + 9) = 0

Reorder the terms:
(4 + n) * x(n + 9) = 0

Reorder the terms:
(4 + n) * x(9 + n) = 0

Reorder the terms for easier multiplication:
x(4 + n)(9 + n) = 0

Multiply (4 + n) * (9 + n)
x(4(9 + n) + n(9 + n)) = 0
x((9 * 4 + n * 4) + n(9 + n)) = 0
x((36 + 4n) + n(9 + n)) = 0
x(36 + 4n + (9 * n + n * n)) = 0
x(36 + 4n + (9n + n2)) = 0

Combine like terms: 4n + 9n = 13n
x(36 + 13n + n2) = 0
(36 * x + 13n * x + n2 * x) = 0

Reorder the terms:
(13nx + n2x + 36x) = 0
(13nx + n2x + 36x) = 0

Solving
13nx + n2x + 36x = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(13n + n2 + 36) = 0

Factor a trinomial.
x((n + 4)(n + 9)) = 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 '(n + 4)' equal to zero and attempt to solve:

Simplifying
n + 4 = 0

Reorder the terms:
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Subproblem 3
Set the factor '(n + 9)' equal to zero and attempt to solve:

Simplifying
n + 9 = 0

Reorder the terms:
9 + n = 0

Solving
9 + n = 0

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

Add '-9' to each side of the equation.
9 + -9 + n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + n = 0 + -9
n = 0 + -9

Combine like terms: 0 + -9 = -9
n = -9

Simplifying
n = -9
Solution
n = {-4, -9}