Find the Roots (Zeros) f(x)=(x-3)(2x-8)

$f (x) = (x - 3) (2 x - 8)$

Step 1

Set $(x - 3) (2 x - 8)$ equal to $0$ .

$(x - 3) (2 x - 8) = 0$

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 $0$ .

$x - 3 = 0$

$2 x - 8 = 0$

Set $x - 3$ equal to $0$ and solve for $x$ .

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $2 x - 8$ equal to $0$ and solve for $x$ .

Set $2 x - 8$ equal to $0$ .

$2 x - 8 = 0$

Solve $2 x - 8 = 0$ for $x$ .

Add $8$ to both sides of the equation.

$2 x = 8$

Divide each term in $2 x = 8$ by $2$ and simplify.

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$

The final solution is all the values that make $(x - 3) (2 x - 8) = 0$ true.

$x = 3, 4$

Step 3