Calculus Examples

$9 x^{2} - 6 x = 0$

Step 1

Factor $3 x$ out of $9 x^{2} - 6 x$ .

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Step 1.1

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

$3 x (3 x) - 6 x = 0$

Step 1.2

Factor $3 x$ out of $- 6 x$ .

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

Step 1.3

Factor $3 x$ out of $3 x (3 x) + 3 x (- 2)$ .

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

Step 2

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

$x = 0$

$3 x - 2 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $3 x - 2$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $3 x - 2$ equal to $0$ .

$3 x - 2 = 0$

Step 4.2

Solve $3 x - 2 = 0$ for $x$ .

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Step 4.2.1

Add $2$ to both sides of the equation.

$3 x = 2$

Step 4.2.2

Divide each term in $3 x = 2$ by $3$ and simplify.

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Step 4.2.2.1

Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Step 4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{3}$

Step 5

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

$x = 0, \frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{2}{3}$

Decimal Form:

$x = 0, 0.\overline{6}$