Algebra Examples

y = - 4 x^{5} (x - 1) {(2 x + 5)}^{4}

$y = - 4 x^{5} (x - 1) {(2 x + 5)}^{4}$

Step 1

Set

- 4 x^{5} (x - 1) {(2 x + 5)}^{4}

$- 4 x^{5} (x - 1) {(2 x + 5)}^{4}$ equal to

0

$0$ .

- 4 x^{5} (x - 1) {(2 x + 5)}^{4} = 0

$- 4 x^{5} (x - 1) {(2 x + 5)}^{4} = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x^{5} = 0

$x^{5} = 0$

x - 1 = 0

$x - 1 = 0$

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

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

Step 2.2

Set

x^{5}

$x^{5}$ equal to

0

$0$ and solve for

x

$x$ .

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Step 2.2.1

Set

x^{5}

$x^{5}$ equal to

0

$0$ .

x^{5} = 0

$x^{5} = 0$

Step 2.2.2

Solve

x^{5} = 0

$x^{5} = 0$ for

x

$x$ .

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Step 2.2.2.1

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

x = \sqrt[5]{0}

$x = \sqrt[5]{0}$

Step 2.2.2.2

Simplify

\sqrt[5]{0}

$\sqrt[5]{0}$ .

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Step 2.2.2.2.1

Rewrite

0

$0$ as

0^{5}

$0^{5}$ .

x = \sqrt[5]{0^{5}}

$x = \sqrt[5]{0^{5}}$

Step 2.2.2.2.2

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

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

Step 2.3

Set

x - 1

$x - 1$ equal to

0

$0$ and solve for

x

$x$ .

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Step 2.3.1

Set

x - 1

$x - 1$ equal to

0

$0$ .

x - 1 = 0

$x - 1 = 0$

Step 2.3.2

Add

1

$1$ to both sides of the equation.

x = 1

$x = 1$

x = 1

$x = 1$

Step 2.4

Set

{(2 x + 5)}^{4}

${(2 x + 5)}^{4}$ equal to

0

$0$ and solve for

x

$x$ .

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Step 2.4.1

Set

{(2 x + 5)}^{4}

${(2 x + 5)}^{4}$ equal to

0

$0$ .

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

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

Step 2.4.2

Solve

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

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

x

$x$ .

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Step 2.4.2.1

Set the

2 x + 5

$2 x + 5$ equal to

0

$0$ .

2 x + 5 = 0

$2 x + 5 = 0$

Step 2.4.2.2

Solve for

x

$x$ .

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Step 2.4.2.2.1

Subtract

5

$5$ from both sides of the equation.

2 x = - 5

$2 x = - 5$

Step 2.4.2.2.2

Divide each term in

2 x = - 5

$2 x = - 5$ by

2

$2$ and simplify.

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Step 2.4.2.2.2.1

Divide each term in

2 x = - 5

$2 x = - 5$ by

2

$2$ .

\frac{2 x}{2} = \frac{- 5}{2}

$\frac{2 x}{2} = \frac{- 5}{2}$

Step 2.4.2.2.2.2

Simplify the left side.

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Step 2.4.2.2.2.2.1

Cancel the common factor of

2

$2$ .

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Step 2.4.2.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 5}{2}$

Step 2.4.2.2.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{- 5}{2}$

Step 2.4.2.2.2.3

Simplify the right side.

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Step 2.4.2.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{5}{2}$

Step 2.5

The final solution is all the values that make

$- 4 x^{5} (x - 1) {(2 x + 5)}^{4} = 0$ true.

$x = 0, 1, - \frac{5}{2}$

Step 3