Find the Roots (Zeros) y=(x+4)(x-5)(x-7)

$y = (x + 4) (x - 5) (x - 7)$

Step 1

Set $(x + 4) (x - 5) (x - 7)$ equal to $0$ .

$(x + 4) (x - 5) (x - 7) = 0$

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 $0$ .

$x + 4 = 0$

$x - 5 = 0$

$x - 7 = 0$

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 $x - 5$ 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 $x - 7$ equal to $0$ and solve for $x$ .

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

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

The final solution is all the values that make $(x + 4) (x - 5) (x - 7) = 0$ true.

$x = - 4, 5, 7$

Step 3