Find the Roots (Zeros) f(x)=-7(x+2)(5x-15)

$f (x) = - 7 (x + 2) (5 x - 15)$

Set $- 7 (x + 2) (5 x - 15)$ equal to $0$ .

$- 7 (x + 2) (5 x - 15) = 0$

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 $0$ .

$x + 2 = 0$

$5 x - 15 = 0$

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.

$x = - 2$

Set $5 x - 15$ equal to $0$ and solve for $x$ .

Set $5 x - 15$ equal to $0$ .

$5 x - 15 = 0$

Solve $5 x - 15 = 0$ for $x$ .

Add $15$ to both sides of the equation.

$5 x = 15$

Divide each term in $5 x = 15$ by $5$ and simplify.

Divide each term in $5 x = 15$ by $5$ .

$\frac{5 x}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{15}{5}$

Divide $x$ by $1$ .

$x = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$x = 3$

The final solution is all the values that make $- 7 (x + 2) (5 x - 15) = 0$ true.

$x = - 2, 3$