Algebra Examples

$(- 5 x - 1) (2 x + 8)$

Step 1

Set $(- 5 x - 1) (2 x + 8)$ equal to $0$ .

$(- 5 x - 1) (2 x + 8) = 0$

Step 2

Solve for $x$ .

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Step 2.1

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

$- 5 x - 1 = 0$

$2 x + 8 = 0$

Step 2.2

Set $- 5 x - 1$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $- 5 x - 1$ equal to $0$ .

$- 5 x - 1 = 0$

Step 2.2.2

Solve $- 5 x - 1 = 0$ for $x$ .

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Step 2.2.2.1

Add $1$ to both sides of the equation.

$- 5 x = 1$

Step 2.2.2.2

Divide each term in $- 5 x = 1$ by $- 5$ and simplify.

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Step 2.2.2.2.1

Divide each term in $- 5 x = 1$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{1}{- 5}$

Step 2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.1

Cancel the common factor of $- 5$ .

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Step 2.2.2.2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{1}{- 5}$

Step 2.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{- 5}$

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

Step 2.3

Set $2 x + 8$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $2 x + 8$ equal to $0$ .

$2 x + 8 = 0$

Step 2.3.2

Solve $2 x + 8 = 0$ for $x$ .

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Step 2.3.2.1

Subtract $8$ from both sides of the equation.

$2 x = - 8$

Step 2.3.2.2

Divide each term in $2 x = - 8$ by $2$ and simplify.

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Step 2.3.2.2.1

Divide each term in $2 x = - 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 2.3.2.2.2

Simplify the left side.

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Step 2.3.2.2.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 2.3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Step 2.3.2.2.3

Simplify the right side.

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Step 2.3.2.2.3.1

Divide $- 8$ by $2$ .

$x = - 4$

Step 2.4

The final solution is all the values that make $(- 5 x - 1) (2 x + 8) = 0$ true.

$x = - \frac{1}{5}, - 4$

Step 3