Solve for n 3n^2=9n

$3 n^{2} = 9 n$

Step 1

Subtract $9 n$ from both sides of the equation.

$3 n^{2} - 9 n = 0$

Step 2

Factor $3 n$ out of $3 n^{2} - 9 n$ .

Factor $3 n$ out of $3 n^{2}$ .

$3 n (n) - 9 n = 0$

Factor $3 n$ out of $- 9 n$ .

$3 n (n) + 3 n (- 3) = 0$

Factor $3 n$ out of $3 n (n) + 3 n (- 3)$ .

$3 n (n - 3) = 0$

Step 3

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

$n = 0$

$n - 3 = 0$

Step 4

Set $n$ equal to $0$ .

$n = 0$

Step 5

Set $n - 3$ equal to $0$ and solve for $n$ .

Set $n - 3$ equal to $0$ .

$n - 3 = 0$

Add $3$ to both sides of the equation.

$n = 3$

Step 6

The final solution is all the values that make $3 n (n - 3) = 0$ true.

$n = 0, 3$