Algebra Examples

$6 h^{5} = 12 h^{3}$

Step 1

Subtract $12 h^{3}$ from both sides of the equation.

$6 h^{5} - 12 h^{3} = 0$

Step 2

Factor $6 h^{3}$ out of $6 h^{5} - 12 h^{3}$ .

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Step 2.1

Factor $6 h^{3}$ out of $6 h^{5}$ .

$6 h^{3} (h^{2}) - 12 h^{3} = 0$

Step 2.2

Factor $6 h^{3}$ out of $- 12 h^{3}$ .

$6 h^{3} (h^{2}) + 6 h^{3} (- 2) = 0$

Step 2.3

Factor $6 h^{3}$ out of $6 h^{3} (h^{2}) + 6 h^{3} (- 2)$ .

$6 h^{3} (h^{2} - 2) = 0$

Step 3

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

$h^{3} = 0$

$h^{2} - 2 = 0$

Step 4

Set $h^{3}$ equal to $0$ and solve for $h$ .

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Step 4.1

Set $h^{3}$ equal to $0$ .

$h^{3} = 0$

Step 4.2

Solve $h^{3} = 0$ for $h$ .

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Step 4.2.1

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

$h = \sqrt[3]{0}$

Step 4.2.2

Simplify $\sqrt[3]{0}$ .

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Step 4.2.2.1

Rewrite $0$ as $0^{3}$ .

$h = \sqrt[3]{0^{3}}$

Step 4.2.2.2

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

$h = 0$

Step 5

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

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Step 5.1

Set $h^{2} - 2$ equal to $0$ .

$h^{2} - 2 = 0$

Step 5.2

Solve $h^{2} - 2 = 0$ for $h$ .

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Step 5.2.1

Add $2$ to both sides of the equation.

$h^{2} = 2$

Step 5.2.2

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

$h = \pm \sqrt{2}$

Step 5.2.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.2.3.1

First, use the positive value of the $\pm$ to find the first solution.

$h = \sqrt{2}$

Step 5.2.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$h = - \sqrt{2}$

Step 5.2.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$h = \sqrt{2}, - \sqrt{2}$

Step 6

The final solution is all the values that make $6 h^{3} (h^{2} - 2) = 0$ true.

$h = 0, \sqrt{2}, - \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$h = 0, \sqrt{2}, - \sqrt{2}$

Decimal Form:

$h = 0, 1.41421356 \dots, - 1.41421356 \dots$