Pre-Algebra Examples

$x^{2} + \frac{7}{3} x = \frac{4}{3} x$

Step 1

Combine $\frac{7}{3}$ and $x$ .

$x^{2} + \frac{7 x}{3} = \frac{4}{3} x$

Step 2

Combine $\frac{4}{3}$ and $x$ .

$x^{2} + \frac{7 x}{3} = \frac{4 x}{3}$

Step 3

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

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Step 3.1

Subtract $\frac{4 x}{3}$ from both sides of the equation.

$x^{2} + \frac{7 x}{3} - \frac{4 x}{3} = 0$

Step 3.2

Combine the numerators over the common denominator.

$x^{2} + \frac{7 x - 4 x}{3} = 0$

Step 3.3

Subtract $4 x$ from $7 x$ .

$x^{2} + \frac{3 x}{3} = 0$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Cancel the common factor.

$x^{2} + \frac{3 x}{3} = 0$

Step 3.4.2

Divide $x$ by $1$ .

$x^{2} + x = 0$

Step 4

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

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Step 4.1

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

$x \cdot x + x = 0$

Step 4.2

Raise $x$ to the power of $1$ .

$x \cdot x + x = 0$

Step 4.3

Factor $x$ out of $x^{1}$ .

$x \cdot x + x \cdot 1 = 0$

Step 4.4

Factor $x$ out of $x \cdot x + x \cdot 1$ .

$x (x + 1) = 0$

Step 5

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

$x = 0$

$x + 1 = 0$

Step 6

Set $x$ equal to $0$ .

$x = 0$

Step 7

Set $x + 1$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 7.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 8

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

$x = 0, - 1$