Solve by Factoring n^4+6n^3=0

$n^{4} + 6 n^{3} = 0$

Step 1

Factor $n^{3}$ out of $n^{4} + 6 n^{3}$ .

Factor $n^{3}$ out of $n^{4}$ .

$n^{3} n + 6 n^{3} = 0$

Factor $n^{3}$ out of $6 n^{3}$ .

$n^{3} n + n^{3} \cdot 6 = 0$

Factor $n^{3}$ out of $n^{3} n + n^{3} \cdot 6$ .

$n^{3} (n + 6) = 0$

Step 2

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

$n^{3} = 0$

$n + 6 = 0$

Step 3

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

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

$n^{3} = 0$

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

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

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

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

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

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

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

$n = 0$

Step 4

Set $n + 6$ equal to $0$ and solve for $n$ .

Set $n + 6$ equal to $0$ .

$n + 6 = 0$

Subtract $6$ from both sides of the equation.

$n = - 6$

Step 5

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

$n = 0, - 6$