Precalculus Examples

$f (x) = 2 x {(x - 4)}^{2} (x - 3^{2})$

Step 1

Set $2 x {(x - 4)}^{2} (x - 3^{2})$ equal to $0$ .

$2 x {(x - 4)}^{2} (x - 3^{2}) = 0$

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 $0$ .

$x = 0$

${(x - 4)}^{2} = 0$

$x - 3^{2} = 0$

Step 2.2

Set $x$ equal to $0$ .

$x = 0$

Step 2.3

Set ${(x - 4)}^{2}$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set ${(x - 4)}^{2}$ equal to $0$ .

${(x - 4)}^{2} = 0$

Step 2.3.2

Solve ${(x - 4)}^{2} = 0$ for $x$ .

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Step 2.3.2.1

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

$x - 4 = 0$

Step 2.3.2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.4

Set $x - 3^{2}$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $x - 3^{2}$ equal to $0$ .

$x - 3^{2} = 0$

Step 2.4.2

Solve $x - 3^{2} = 0$ for $x$ .

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Step 2.4.2.1

Simplify each term.

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Step 2.4.2.1.1

Raise $3$ to the power of $2$ .

$x - 1 \cdot 9 = 0$

Step 2.4.2.1.2

Multiply $- 1$ by $9$ .

$x - 9 = 0$

Step 2.4.2.2

Add $9$ to both sides of the equation.

$x = 9$

Step 2.5

The final solution is all the values that make $2 x {(x - 4)}^{2} (x - 3^{2}) = 0$ true.

$x = 0, 4, 9$

Step 3