Finite Math Examples

$f (x) = - 4 {(x - 4)}^{3} {(x + 5)}^{2} x^{4}$

Step 1

Set $- 4 {(x - 4)}^{3} {(x + 5)}^{2} x^{4}$ equal to $0$ .

$- 4 {(x - 4)}^{3} {(x + 5)}^{2} x^{4} = 0$

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 $0$ .

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

${(x + 5)}^{2} = 0$

$x^{4} = 0$

Step 2.2

Set ${(x - 4)}^{3}$ equal to $0$ and solve for $x$ .

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Step 2.2.1

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

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

Step 2.2.2

Solve ${(x - 4)}^{3} = 0$ for $x$ .

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Step 2.2.2.1

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

$x - 4 = 0$

Step 2.2.2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.3

Set ${(x + 5)}^{2}$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set ${(x + 5)}^{2}$ equal to $0$ .

${(x + 5)}^{2} = 0$

Step 2.3.2

Solve ${(x + 5)}^{2} = 0$ for $x$ .

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Step 2.3.2.1

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

$x + 5 = 0$

Step 2.3.2.2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 2.4

Set $x^{4}$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $x^{4}$ equal to $0$ .

$x^{4} = 0$

Step 2.4.2

Solve $x^{4} = 0$ for $x$ .

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Step 2.4.2.1

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

$x = \pm \sqrt[4]{0}$

Step 2.4.2.2

Simplify $\pm \sqrt[4]{0}$ .

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Step 2.4.2.2.1

Rewrite $0$ as $0^{4}$ .

$x = \pm \sqrt[4]{0^{4}}$

Step 2.4.2.2.2

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

$x = \pm 0$

Step 2.4.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 2.5

The final solution is all the values that make $- 4 {(x - 4)}^{3} {(x + 5)}^{2} x^{4} = 0$ true.

$x = 4, - 5, 0$

Step 3