Find the Roots (Zeros) f(x)=-x(x+2)(x-2)(x+1)

$f (x) = - x (x + 2) (x - 2) (x + 1)$

Step 1

Set $- x (x + 2) (x - 2) (x + 1)$ equal to $0$ .

$- x (x + 2) (x - 2) (x + 1) = 0$

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 $0$ .

$x = 0$

$x + 2 = 0$

$x - 2 = 0$

$x + 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $- x (x + 2) (x - 2) (x + 1) = 0$ true.

$x = 0, - 2, 2, - 1$

Step 3