Pre-Algebra Examples

$(x - 5) (5 x - 8) = 0$

Step 1

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

$x - 5 = 0$

$5 x - 8 = 0$

Step 2

Set $x - 5$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Step 2.2

Add $5$ to both sides of the equation.

$x = 5$

Step 3

Set $5 x - 8$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $5 x - 8$ equal to $0$ .

$5 x - 8 = 0$

Step 3.2

Solve $5 x - 8 = 0$ for $x$ .

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Step 3.2.1

Add $8$ to both sides of the equation.

$5 x = 8$

Step 3.2.2

Divide each term in $5 x = 8$ by $5$ and simplify.

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Step 3.2.2.1

Divide each term in $5 x = 8$ by $5$ .

$\frac{5 x}{5} = \frac{8}{5}$

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{8}{5}$

Step 3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{5}$

Step 4

The final solution is all the values that make $(x - 5) (5 x - 8) = 0$ true.

$x = 5, \frac{8}{5}$