Pre-Algebra Examples

$x^{2} + \frac{23}{9} x = \frac{5}{9} x$

Step 1

Combine $\frac{23}{9}$ and $x$ .

$x^{2} + \frac{23 x}{9} = \frac{5}{9} x$

Step 2

Combine $\frac{5}{9}$ and $x$ .

$x^{2} + \frac{23 x}{9} = \frac{5 x}{9}$

Step 3

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1

Subtract $\frac{5 x}{9}$ from both sides of the equation.

$x^{2} + \frac{23 x}{9} - \frac{5 x}{9} = 0$

Step 3.2

Combine the numerators over the common denominator.

$x^{2} + \frac{23 x - 5 x}{9} = 0$

Step 3.3

Subtract $5 x$ from $23 x$ .

$x^{2} + \frac{18 x}{9} = 0$

Step 3.4

Cancel the common factor of $18$ and $9$ .

Tap for more steps...

Step 3.4.1

Factor $9$ out of $18 x$ .

$x^{2} + \frac{9 (2 x)}{9} = 0$

Step 3.4.2

Cancel the common factors.

Tap for more steps...

Step 3.4.2.1

Factor $9$ out of $9$ .

$x^{2} + \frac{9 (2 x)}{9 (1)} = 0$

Step 3.4.2.2

Cancel the common factor.

$x^{2} + \frac{9 (2 x)}{9 \cdot 1} = 0$

Step 3.4.2.3

Rewrite the expression.

$x^{2} + \frac{2 x}{1} = 0$

Step 3.4.2.4

Divide $2 x$ by $1$ .

$x^{2} + 2 x = 0$

Step 4

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

Tap for more steps...

Step 4.1

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

$x \cdot x + 2 x = 0$

Step 4.2

Factor $x$ out of $2 x$ .

$x \cdot x + x \cdot 2 = 0$

Step 4.3

Factor $x$ out of $x \cdot x + x \cdot 2$ .

$x (x + 2) = 0$

Step 5

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

$x = 0$

$x + 2 = 0$

Step 6

Set $x$ equal to $0$ .

$x = 0$

Step 7

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

Tap for more steps...

Step 7.1

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

$x + 2 = 0$

Step 7.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 8

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

$x = 0, - 2$