Solve for x 0=9x^2-3x

$0 = 9 x^{2} - 3 x$

Step 1

Rewrite the equation as $9 x^{2} - 3 x = 0$ .

$9 x^{2} - 3 x = 0$

Step 2

Factor $3 x$ out of $9 x^{2} - 3 x$ .

Factor $3 x$ out of $9 x^{2}$ .

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

Factor $3 x$ out of $- 3 x$ .

$3 x (3 x) + 3 x (- 1) = 0$

Factor $3 x$ out of $3 x (3 x) + 3 x (- 1)$ .

$3 x (3 x - 1) = 0$

Step 3

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

$x = 0$

$3 x - 1 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $3 x - 1$ equal to $0$ and solve for $x$ .

Set $3 x - 1$ equal to $0$ .

$3 x - 1 = 0$

Solve $3 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$3 x = 1$

Divide each term in $3 x = 1$ by $3$ and simplify.

Divide each term in $3 x = 1$ by $3$ .

$\frac{3 x}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{1}{3}$

Divide $x$ by $1$ .

$x = \frac{1}{3}$

Step 6

The final solution is all the values that make $3 x (3 x - 1) = 0$ true.

$x = 0, \frac{1}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{1}{3}$

Decimal Form:

$x = 0, 0.\overline{3}$