Find the Roots (Zeros) f(x)=(2x+6)(x-4)

$f (x) = (2 x + 6) (x - 4)$

Step 1

Set $(2 x + 6) (x - 4)$ equal to $0$ .

$(2 x + 6) (x - 4) = 0$

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 $0$ .

$2 x + 6 = 0$

$x - 4 = 0$

Set $2 x + 6$ equal to $0$ and solve for $x$ .

Set $2 x + 6$ equal to $0$ .

$2 x + 6 = 0$

Solve $2 x + 6 = 0$ for $x$ .

Subtract $6$ from both sides of the equation.

$2 x = - 6$

Divide each term in $2 x = - 6$ by $2$ and simplify.

Divide each term in $2 x = - 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$x = - 3$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $(2 x + 6) (x - 4) = 0$ true.

$x = - 3, 4$

Step 3