Pre-Algebra Examples

$(x - 4) (4 x + 5) = 0$

Step 1

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

$x - 4 = 0$

$4 x + 5 = 0$

Step 2

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 3

Set $4 x + 5$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $4 x + 5$ equal to $0$ .

$4 x + 5 = 0$

Step 3.2

Solve $4 x + 5 = 0$ for $x$ .

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Step 3.2.1

Subtract $5$ from both sides of the equation.

$4 x = - 5$

Step 3.2.2

Divide each term in $4 x = - 5$ by $4$ and simplify.

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Step 3.2.2.1

Divide each term in $4 x = - 5$ by $4$ .

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

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 3.2.2.3

Simplify the right side.

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Step 3.2.2.3.1

Move the negative in front of the fraction.

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

Step 4

The final solution is all the values that make $(x - 4) (4 x + 5) = 0$ true.

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