Find the Roots (Zeros) (-x-2)(-2x-3)

$(- x - 2) (- 2 x - 3)$

Set $(- x - 2) (- 2 x - 3)$ equal to $0$ .

$(- x - 2) (- 2 x - 3) = 0$

Solve for $x$ .

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

$- x - 2 = 0$

$- 2 x - 3 = 0$

Set $- x - 2$ equal to $0$ and solve for $x$ .

Set $- x - 2$ equal to $0$ .

$- x - 2 = 0$

Solve $- x - 2 = 0$ for $x$ .

Add $2$ to both sides of the equation.

$- x = 2$

Divide each term in $- x = 2$ by $- 1$ and simplify.

Divide each term in $- x = 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$x = - 2$

Set $- 2 x - 3$ equal to $0$ and solve for $x$ .

Set $- 2 x - 3$ equal to $0$ .

$- 2 x - 3 = 0$

Solve $- 2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$- 2 x = 3$

Divide each term in $- 2 x = 3$ by $- 2$ and simplify.

Divide each term in $- 2 x = 3$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{3}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{3}{- 2}$

Divide $x$ by $1$ .

$x = \frac{3}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

The final solution is all the values that make $(- x - 2) (- 2 x - 3) = 0$ true.

$x = - 2, - \frac{3}{2}$