Solve for m 9m^5=27m^3

$9 m^{5} = 27 m^{3}$

Step 1

Subtract $27 m^{3}$ from both sides of the equation.

$9 m^{5} - 27 m^{3} = 0$

Step 2

Factor $9 m^{3}$ out of $9 m^{5} - 27 m^{3}$ .

Factor $9 m^{3}$ out of $9 m^{5}$ .

$9 m^{3} (m^{2}) - 27 m^{3} = 0$

Factor $9 m^{3}$ out of $- 27 m^{3}$ .

$9 m^{3} (m^{2}) + 9 m^{3} (- 3) = 0$

Factor $9 m^{3}$ out of $9 m^{3} (m^{2}) + 9 m^{3} (- 3)$ .

$9 m^{3} (m^{2} - 3) = 0$

Step 3

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

$m^{3} = 0$

$m^{2} - 3 = 0$

Step 4

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

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

$m^{3} = 0$

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

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

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

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

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

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

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

$m = 0$

Step 5

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

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

$m^{2} - 3 = 0$

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

Add $3$ to both sides of the equation.

$m^{2} = 3$

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

$m = \pm \sqrt{3}$

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

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

$m = \sqrt{3}$

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

$m = - \sqrt{3}$

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

$m = \sqrt{3}, - \sqrt{3}$

Step 6

The final solution is all the values that make $9 m^{3} (m^{2} - 3) = 0$ true.

$m = 0, \sqrt{3}, - \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$m = 0, \sqrt{3}, - \sqrt{3}$

Decimal Form:

$m = 0, 1.73205080 \dots, - 1.73205080 \dots$

Solve for m 9m^5=27m^3

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