Solve for p 3p^3=21p

$3 p^{3} = 21 p$

Subtract $21 p$ from both sides of the equation.

$3 p^{3} - 21 p = 0$

Factor $3 p$ out of $3 p^{3} - 21 p$ .

Factor $3 p$ out of $3 p^{3}$ .

$3 p (p^{2}) - 21 p = 0$

Factor $3 p$ out of $- 21 p$ .

$3 p (p^{2}) + 3 p (- 7) = 0$

Factor $3 p$ out of $3 p (p^{2}) + 3 p (- 7)$ .

$3 p (p^{2} - 7) = 0$

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

$p = 0$

$p^{2} - 7 = 0$

Set $p$ equal to $0$ .

$p = 0$

Set $p^{2} - 7$ equal to $0$ and solve for $p$ .

Set $p^{2} - 7$ equal to $0$ .

$p^{2} - 7 = 0$

Solve $p^{2} - 7 = 0$ for $p$ .

Add $7$ to both sides of the equation.

$p^{2} = 7$

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

$p = \pm \sqrt{7}$

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.

$p = \sqrt{7}$

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

$p = - \sqrt{7}$

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

$p = \sqrt{7}, - \sqrt{7}$

The final solution is all the values that make $3 p (p^{2} - 7) = 0$ true.

$p = 0, \sqrt{7}, - \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$p = 0, \sqrt{7}, - \sqrt{7}$

Decimal Form:

$p = 0, 2.64575131 \dots, - 2.64575131 \dots$