Algebra Examples

$(0.3 x^{2} - 3 x) (5 x^{3} - 0.2 x^{2}) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$0.3 x^{2} - 3 x = 0$

$5 x^{3} - 0.2 x^{2} = 0$

Step 2

Set $0.3 x^{2} - 3 x$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $0.3 x^{2} - 3 x$ equal to $0$ .

$0.3 x^{2} - 3 x = 0$

Step 2.2

Solve $0.3 x^{2} - 3 x = 0$ for $x$ .

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Step 2.2.1

Factor $0.3 x$ out of $0.3 x^{2} - 3 x$ .

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Step 2.2.1.1

Factor $0.3 x$ out of $0.3 x^{2}$ .

$0.3 x (x) - 3 x = 0$

Step 2.2.1.2

Factor $0.3 x$ out of $- 3 x$ .

$0.3 x (x) + 0.3 x (- 10) = 0$

Step 2.2.1.3

Factor $0.3 x$ out of $0.3 x (x) + 0.3 x (- 10)$ .

$0.3 x (x - 10) = 0$

Step 2.2.2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 10 = 0$

Step 2.2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.2.4

Set $x - 10$ equal to $0$ and solve for $x$ .

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Step 2.2.4.1

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Step 2.2.4.2

Add $10$ to both sides of the equation.

$x = 10$

Step 2.2.5

The final solution is all the values that make $0.3 x (x - 10) = 0$ true.

$x = 0, 10$

Step 3

Set $5 x^{3} - 0.2 x^{2}$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $5 x^{3} - 0.2 x^{2}$ equal to $0$ .

$5 x^{3} - 0.2 x^{2} = 0$

Step 3.2

Solve $5 x^{3} - 0.2 x^{2} = 0$ for $x$ .

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Step 3.2.1

Factor $0.2 x^{2}$ out of $5 x^{3} - 0.2 x^{2}$ .

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Step 3.2.1.1

Factor $0.2 x^{2}$ out of $5 x^{3}$ .

$0.2 x^{2} (25 x) - 0.2 x^{2} = 0$

Step 3.2.1.2

Factor $0.2 x^{2}$ out of $- 0.2 x^{2}$ .

$0.2 x^{2} (25 x) + 0.2 x^{2} (- 1) = 0$

Step 3.2.1.3

Factor $0.2 x^{2}$ out of $0.2 x^{2} (25 x) + 0.2 x^{2} (- 1)$ .

$0.2 x^{2} (25 x - 1) = 0$

Step 3.2.2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x^{2} = 0$

$25 x - 1 = 0$

Step 3.2.3

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

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Step 3.2.3.1

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

$x^{2} = 0$

Step 3.2.3.2

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

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Step 3.2.3.2.1

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

$x = \pm \sqrt{0}$

Step 3.2.3.2.2

Simplify $\pm \sqrt{0}$ .

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Step 3.2.3.2.2.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 3.2.3.2.2.2

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

$x = \pm 0$

Step 3.2.3.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 3.2.4

Set $25 x - 1$ equal to $0$ and solve for $x$ .

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Step 3.2.4.1

Set $25 x - 1$ equal to $0$ .

$25 x - 1 = 0$

Step 3.2.4.2

Solve $25 x - 1 = 0$ for $x$ .

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Step 3.2.4.2.1

Add $1$ to both sides of the equation.

$25 x = 1$

Step 3.2.4.2.2

Divide each term in $25 x = 1$ by $25$ and simplify.

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Step 3.2.4.2.2.1

Divide each term in $25 x = 1$ by $25$ .

$\frac{25 x}{25} = \frac{1}{25}$

Step 3.2.4.2.2.2

Simplify the left side.

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Step 3.2.4.2.2.2.1

Cancel the common factor of $25$ .

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Step 3.2.4.2.2.2.1.1

Cancel the common factor.

$\frac{25 x}{25} = \frac{1}{25}$

Step 3.2.4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{25}$

Step 3.2.5

The final solution is all the values that make $0.2 x^{2} (25 x - 1) = 0$ true.

$x = 0, \frac{1}{25}$

Step 4

The final solution is all the values that make $(0.3 x^{2} - 3 x) (5 x^{3} - 0.2 x^{2}) = 0$ true.

$x = 0, 10, \frac{1}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 0, 10, \frac{1}{25}$

Decimal Form:

$x = 0, 10, 0.04$