Algebra Examples

$p (x) = (9 x + 3) (x^{2} - 9)$

Step 1

Set $(9 x + 3) (x^{2} - 9)$ equal to $0$ .

$(9 x + 3) (x^{2} - 9) = 0$

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 $0$ .

$9 x + 3 = 0$

$x^{2} - 9 = 0$

Step 2.2

Set $9 x + 3$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $9 x + 3$ equal to $0$ .

$9 x + 3 = 0$

Step 2.2.2

Solve $9 x + 3 = 0$ for $x$ .

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Step 2.2.2.1

Subtract $3$ from both sides of the equation.

$9 x = - 3$

Step 2.2.2.2

Divide each term in $9 x = - 3$ by $9$ and simplify.

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Step 2.2.2.2.1

Divide each term in $9 x = - 3$ by $9$ .

$\frac{9 x}{9} = \frac{- 3}{9}$

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 $9$ .

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Step 2.2.2.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 3}{9}$

Step 2.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{9}$

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

Cancel the common factor of $- 3$ and $9$ .

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Step 2.2.2.2.3.1.1

Factor $3$ out of $- 3$ .

$x = \frac{3 (- 1)}{9}$

Step 2.2.2.2.3.1.2

Cancel the common factors.

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Step 2.2.2.2.3.1.2.1

Factor $3$ out of $9$ .

$x = \frac{3 \cdot - 1}{3 \cdot 3}$

Step 2.2.2.2.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot - 1}{3 \cdot 3}$

Step 2.2.2.2.3.1.2.3

Rewrite the expression.

$x = \frac{- 1}{3}$

Step 2.2.2.2.3.2

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

Step 2.3

Set $x^{2} - 9$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x^{2} - 9$ equal to $0$ .

$x^{2} - 9 = 0$

Step 2.3.2

Solve $x^{2} - 9 = 0$ for $x$ .

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Step 2.3.2.1

Add $9$ to both sides of the equation.

$x^{2} = 9$

Step 2.3.2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{9}$

Step 2.3.2.3

Simplify $\pm \sqrt{9}$ .

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Step 2.3.2.3.1

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Step 2.3.2.3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

Step 2.3.2.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.3.2.4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Step 2.3.2.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

Step 2.3.2.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$

Step 2.4

The final solution is all the values that make $(9 x + 3) (x^{2} - 9) = 0$ true.

$x = - \frac{1}{3}, 3, - 3$

Step 3