Find the Roots (Zeros) p(x)=x(x-5)(x-2)(x+3)

$p (x) = x (x - 5) (x - 2) (x + 3)$

Step 1

Set $x (x - 5) (x - 2) (x + 3)$ equal to $0$ .

$x (x - 5) (x - 2) (x + 3) = 0$

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 $0$ .

$x = 0$

$x - 5 = 0$

$x - 2 = 0$

$x + 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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 $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

The final solution is all the values that make $x (x - 5) (x - 2) (x + 3) = 0$ true.

$x = 0, 5, 2, - 3$

Step 3