Pre-Algebra Examples

$(\frac{x}{5} - 5) \cdot (\frac{x}{5} + 5) = 0$

Step 1

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

$\frac{x}{5} - 5 = 0$

$\frac{x}{5} + 5 = 0$

Step 2

Set $\frac{x}{5} - 5$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $\frac{x}{5} - 5$ equal to $0$ .

$\frac{x}{5} - 5 = 0$

Step 2.2

Solve $\frac{x}{5} - 5 = 0$ for $x$ .

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Step 2.2.1

Add $5$ to both sides of the equation.

$\frac{x}{5} = 5$

Step 2.2.2

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 \cdot 5$

Step 2.2.3

Simplify both sides of the equation.

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Step 2.2.3.1

Simplify the left side.

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Step 2.2.3.1.1

Cancel the common factor of $5$ .

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Step 2.2.3.1.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 \cdot 5$

Step 2.2.3.1.1.2

Rewrite the expression.

$x = 5 \cdot 5$

Step 2.2.3.2

Simplify the right side.

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Step 2.2.3.2.1

Multiply $5$ by $5$ .

$x = 25$

Step 3

Set $\frac{x}{5} + 5$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $\frac{x}{5} + 5$ equal to $0$ .

$\frac{x}{5} + 5 = 0$

Step 3.2

Solve $\frac{x}{5} + 5 = 0$ for $x$ .

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Step 3.2.1

Subtract $5$ from both sides of the equation.

$\frac{x}{5} = - 5$

Step 3.2.2

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 \cdot - 5$

Step 3.2.3

Simplify both sides of the equation.

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Step 3.2.3.1

Simplify the left side.

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Step 3.2.3.1.1

Cancel the common factor of $5$ .

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Step 3.2.3.1.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 \cdot - 5$

Step 3.2.3.1.1.2

Rewrite the expression.

$x = 5 \cdot - 5$

Step 3.2.3.2

Simplify the right side.

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Step 3.2.3.2.1

Multiply $5$ by $- 5$ .

$x = - 25$

Step 4

The final solution is all the values that make $(\frac{x}{5} - 5) \cdot (\frac{x}{5} + 5) = 0$ true.

$x = 25, - 25$