Solve for n -9(n+4)=-5n-(4n+36)

$- 9 (n + 4) = - 5 n - (4 n + 36)$

Step 1

Since $n$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 5 n - (4 n + 36) = - 9 (n + 4)$

Step 2

Simplify $- 5 n - (4 n + 36)$ .

Simplify each term.

Apply the distributive property.

$- 5 n - (4 n) - 1 \cdot 36 = - 9 (n + 4)$

Multiply $4$ by $- 1$ .

$- 5 n - 4 n - 1 \cdot 36 = - 9 (n + 4)$

Multiply $- 1$ by $36$ .

$- 5 n - 4 n - 36 = - 9 (n + 4)$

Subtract $4 n$ from $- 5 n$ .

$- 9 n - 36 = - 9 (n + 4)$

Step 3

Simplify $- 9 (n + 4)$ .

Apply the distributive property.

$- 9 n - 36 = - 9 n - 9 \cdot 4$

Multiply $- 9$ by $4$ .

$- 9 n - 36 = - 9 n - 36$

Step 4

Move all terms containing $n$ to the left side of the equation.

Add $9 n$ to both sides of the equation.

$- 9 n - 36 + 9 n = - 36$

Combine the opposite terms in $- 9 n - 36 + 9 n$ .

Add $- 9 n$ and $9 n$ .

$0 - 36 = - 36$

Subtract $36$ from $0$ .

$- 36 = - 36$

Step 5

Since $- 36 = - 36$ , the equation will always be true for any value of $n$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$