Find the Roots (Zeros) f(x)=(x(x+7)(x+2))/((x-4)(x+4))

$f (x) = \frac{x (x + 7) (x + 2)}{(x - 4) (x + 4)}$

Step 1

Set $\frac{x (x + 7) (x + 2)}{(x - 4) (x + 4)}$ equal to $0$ .

$\frac{x (x + 7) (x + 2)}{(x - 4) (x + 4)} = 0$

Step 2

Solve for $x$ .

Set the numerator equal to zero.

$x (x + 7) (x + 2) = 0$

Solve the equation for $x$ .

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

$x = 0$

$x + 7 = 0$

$x + 2 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

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.

$x = - 2$

The final solution is all the values that make $x (x + 7) (x + 2) = 0$ true.

$x = 0, - 7, - 2$

Step 3