Find the Roots (Zeros) (x-2)(x^2-9)

$(x - 2) (x^{2} - 9)$

Step 1

Set $(x - 2) (x^{2} - 9)$ equal to $0$ .

$(x - 2) (x^{2} - 9) = 0$

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 $0$ .

$x - 2 = 0$

$x^{2} - 9 = 0$

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 $x^{2} - 9$ equal to $0$ and solve for $x$ .

Set $x^{2} - 9$ equal to $0$ .

$x^{2} - 9 = 0$

Solve $x^{2} - 9 = 0$ for $x$ .

Add $9$ to both sides of the equation.

$x^{2} = 9$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$

The final solution is all the values that make $(x - 2) (x^{2} - 9) = 0$ true.

$x = 2, 3, - 3$

Step 3