Finite Math Examples

$(x - 9) (2 x + 9) = 0$

Step 1

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

$x - 9 = 0$

$2 x + 9 = 0$

Step 2

Set $x - 9$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Step 2.2

Add $9$ to both sides of the equation.

$x = 9$

Step 3

Set $2 x + 9$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $2 x + 9$ equal to $0$ .

$2 x + 9 = 0$

Step 3.2

Solve $2 x + 9 = 0$ for $x$ .

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Step 3.2.1

Subtract $9$ from both sides of the equation.

$2 x = - 9$

Step 3.2.2

Divide each term in $2 x = - 9$ by $2$ and simplify.

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Step 3.2.2.1

Divide each term in $2 x = - 9$ by $2$ .

$\frac{2 x}{2} = \frac{- 9}{2}$

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 9}{2}$

Step 3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 9}{2}$

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.

$x = - \frac{9}{2}$

Step 4

The final solution is all the values that make $(x - 9) (2 x + 9) = 0$ true.

$x = 9, - \frac{9}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 9, - \frac{9}{2}$

Decimal Form:

$x = 9, - 4.5$

Mixed Number Form:

$x = 9, - 4 \frac{1}{2}$