Find the Roots (Zeros) f(x)=(4x^2-36x)/(x-9)

$f (x) = \frac{4 x^{2} - 36 x}{x - 9}$

Step 1

Set $\frac{4 x^{2} - 36 x}{x - 9}$ equal to $0$ .

$\frac{4 x^{2} - 36 x}{x - 9} = 0$

Step 2

Solve for $x$ .

Set the numerator equal to zero.

$4 x^{2} - 36 x = 0$

Solve the equation for $x$ .

Factor $4 x$ out of $4 x^{2} - 36 x$ .

Factor $4 x$ out of $4 x^{2}$ .

$4 x (x) - 36 x = 0$

Factor $4 x$ out of $- 36 x$ .

$4 x (x) + 4 x (- 9) = 0$

Factor $4 x$ out of $4 x (x) + 4 x (- 9)$ .

$4 x (x - 9) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 9 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

The final solution is all the values that make $4 x (x - 9) = 0$ true.

$x = 0, 9$

Exclude the solutions that do not make $\frac{4 x^{2} - 36 x}{x - 9} = 0$ true.

$x = 0$

Step 3