Solve by Factoring (n+2)(2n+5)=0

$(n + 2) (2 n + 5) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$n + 2 = 0$

$2 n + 5 = 0$

Step 2

Set $n + 2$ equal to $0$ and solve for $n$ .

Set $n + 2$ equal to $0$ .

$n + 2 = 0$

Subtract $2$ from both sides of the equation.

$n = - 2$

Step 3

Set $2 n + 5$ equal to $0$ and solve for $n$ .

Set $2 n + 5$ equal to $0$ .

$2 n + 5 = 0$

Solve $2 n + 5 = 0$ for $n$ .

Subtract $5$ from both sides of the equation.

$2 n = - 5$

Divide each term in $2 n = - 5$ by $2$ and simplify.

Divide each term in $2 n = - 5$ by $2$ .

$\frac{2 n}{2} = \frac{- 5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} = \frac{- 5}{2}$

Divide $n$ by $1$ .

$n = \frac{- 5}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$n = - \frac{5}{2}$

Step 4

The final solution is all the values that make $(n + 2) (2 n + 5) = 0$ true.

$n = - 2, - \frac{5}{2}$