Solve by Factoring 5w^3=50w

$5 w^{3} = 50 w$

Subtract $50 w$ from both sides of the equation.

$5 w^{3} - 50 w = 0$

Factor $5 w$ out of $5 w^{3} - 50 w$ .

Factor $5 w$ out of $5 w^{3}$ .

$5 w (w^{2}) - 50 w = 0$

Factor $5 w$ out of $- 50 w$ .

$5 w (w^{2}) + 5 w (- 10) = 0$

Factor $5 w$ out of $5 w (w^{2}) + 5 w (- 10)$ .

$5 w (w^{2} - 10) = 0$

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

$w = 0$

$w^{2} - 10 = 0$

Set $w$ equal to $0$ .

$w = 0$

Set $w^{2} - 10$ equal to $0$ and solve for $w$ .

Set $w^{2} - 10$ equal to $0$ .

$w^{2} - 10 = 0$

Solve $w^{2} - 10 = 0$ for $w$ .

Add $10$ to both sides of the equation.

$w^{2} = 10$

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

$w = \pm \sqrt{10}$

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.

$w = \sqrt{10}$

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

$w = - \sqrt{10}$

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

$w = \sqrt{10}, - \sqrt{10}$

The final solution is all the values that make $5 w (w^{2} - 10) = 0$ true.

$w = 0, \sqrt{10}, - \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$w = 0, \sqrt{10}, - \sqrt{10}$

Decimal Form:

$w = 0, 3.16227766 \dots, - 3.16227766 \dots$