Find the Roots (Zeros) -x(x+4)(x+2/3)(x-9)

$- x (x + 4) (x + \frac{2}{3}) (x - 9)$

Step 1

Set $- x (x + 4) (x + \frac{2}{3}) (x - 9)$ equal to $0$ .

$- x (x + 4) (x + \frac{2}{3}) (x - 9) = 0$

Step 2

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 $0$ .

$x = 0$

$x + 4 = 0$

$x + \frac{2}{3} = 0$

$x - 9 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Set $x + \frac{2}{3}$ equal to $0$ and solve for $x$ .

Set $x + \frac{2}{3}$ equal to $0$ .

$x + \frac{2}{3} = 0$

Subtract $\frac{2}{3}$ from both sides of the equation.

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

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

The final solution is all the values that make $- x (x + 4) (x + \frac{2}{3}) (x - 9) = 0$ true.

$x = 0, - 4, - \frac{2}{3}, 9$

Step 3