Algebra Examples

$5 n^{2} = 9 n$

Step 1

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

$5 n^{2} - 9 n = 0$

Step 2

Factor $n$ out of $5 n^{2} - 9 n$ .

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Step 2.1

Factor $n$ out of $5 n^{2}$ .

$n (5 n) - 9 n = 0$

Step 2.2

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

$n (5 n) + n \cdot - 9 = 0$

Step 2.3

Factor $n$ out of $n (5 n) + n \cdot - 9$ .

$n (5 n - 9) = 0$

Step 3

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

$n = 0$

$5 n - 9 = 0$

Step 4

Set $n$ equal to $0$ .

$n = 0$

Step 5

Set $5 n - 9$ equal to $0$ and solve for $n$ .

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Step 5.1

Set $5 n - 9$ equal to $0$ .

$5 n - 9 = 0$

Step 5.2

Solve $5 n - 9 = 0$ for $n$ .

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Step 5.2.1

Add $9$ to both sides of the equation.

$5 n = 9$

Step 5.2.2

Divide each term in $5 n = 9$ by $5$ and simplify.

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Step 5.2.2.1

Divide each term in $5 n = 9$ by $5$ .

$\frac{5 n}{5} = \frac{9}{5}$

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Cancel the common factor of $5$ .

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Step 5.2.2.2.1.1

Cancel the common factor.

$\frac{5 n}{5} = \frac{9}{5}$

Step 5.2.2.2.1.2

Divide $n$ by $1$ .

$n = \frac{9}{5}$

Step 6

The final solution is all the values that make $n (5 n - 9) = 0$ true.

$n = 0, \frac{9}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$n = 0, \frac{9}{5}$

Decimal Form:

$n = 0, 1.8$

Mixed Number Form:

$n = 0, 1 \frac{4}{5}$