Find the Roots (Zeros) y=(x+5)(x-6)(x-7)

$y = (x + 5) (x - 6) (x - 7)$

Step 1

Set $(x + 5) (x - 6) (x - 7)$ equal to $0$ .

$(x + 5) (x - 6) (x - 7) = 0$

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 $0$ .

$x + 5 = 0$

$x - 6 = 0$

$x - 7 = 0$

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

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

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

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 $(x + 5) (x - 6) (x - 7) = 0$ true.

$x = - 5, 6, 7$

Step 3