Algebra Examples

$f (x) = {(x + 8)}^{2} (2 - x)$

Step 1

Set ${(x + 8)}^{2} (2 - x)$ equal to $0$ .

${(x + 8)}^{2} (2 - x) = 0$

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 $0$ .

${(x + 8)}^{2} = 0$

$2 - x = 0$

Step 2.2

Set ${(x + 8)}^{2}$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set ${(x + 8)}^{2}$ equal to $0$ .

${(x + 8)}^{2} = 0$

Step 2.2.2

Solve ${(x + 8)}^{2} = 0$ for $x$ .

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Step 2.2.2.1

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

$x + 8 = 0$

Step 2.2.2.2

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 2.3

Set $2 - x$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $2 - x$ equal to $0$ .

$2 - x = 0$

Step 2.3.2

Solve $2 - x = 0$ for $x$ .

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Step 2.3.2.1

Subtract $2$ from both sides of the equation.

$- x = - 2$

Step 2.3.2.2

Divide each term in $- x = - 2$ by $- 1$ and simplify.

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Step 2.3.2.2.1

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Step 2.3.2.2.2

Simplify the left side.

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Step 2.3.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Step 2.3.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Step 2.3.2.2.3

Simplify the right side.

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Step 2.3.2.2.3.1

Divide $- 2$ by $- 1$ .

$x = 2$

Step 2.4

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

$x = - 8, 2$

Step 3