# How do you solve 5/(n+10)=3/(3n+6)?

Jun 1, 2017

$n = 0$

#### Explanation:

We have: $\frac{5}{n + 10} = \frac{3}{3 n + 6}$

Let's cross-multiply:

$R i g h t a r r o w 5 \left(3 n + 6\right) = 3 \left(n + 10\right)$

Then, let's expand the parentheses:

$R i g h t a r r o w 15 n + 30 = 3 n + 30$

Now, let's subtract $3 n + 30$ from both sides of the equation:

$R i g h t a r r o w 15 n + 30 - \left(3 n + 30\right) = 3 n + 30 - \left(3 n + 30\right)$

$R i g h t a r r o w 15 n - 3 n + 30 - 30 = 3 n - 3 n + 30 - 30$

$R i g h t a r r o w 12 n = 0$

Finally, to solve for $n$, let's divide both sides by $12$:

$R i g h t a r r o w \frac{12 n}{12} = \frac{0}{12}$

$\therefore n = 0$

Therefore, the solution to the equation is $n = 0$.

Jun 1, 2017

$n = 0$

#### Explanation:

Use cross multiplication.

$5 \left(3 n + 6\right) = 3 \left(n + 10\right)$

Use the Distributive property:

$15 n + 30 = 3 n + 30$

Group like terms together:

$15 n - 3 n + 30 - 30 = 0$

$12 n = 0$

$n = 0$