Solve for n (2n-4)/5=(3n+3)/10

$\frac{2 n - 4}{5} = \frac{3 n + 3}{10}$

Step 1

Simplify both sides.

Factor $2$ out of $2 n - 4$ .

Factor $2$ out of $2 n$ .

$\frac{2 (n) - 4}{5} = \frac{3 n + 3}{10}$

Factor $2$ out of $- 4$ .

$\frac{2 n + 2 \cdot - 2}{5} = \frac{3 n + 3}{10}$

Factor $2$ out of $2 n + 2 \cdot - 2$ .

$\frac{2 (n - 2)}{5} = \frac{3 n + 3}{10}$

Factor $3$ out of $3 n + 3$ .

Factor $3$ out of $3 n$ .

$\frac{2 (n - 2)}{5} = \frac{3 (n) + 3}{10}$

Factor $3$ out of $3$ .

$\frac{2 (n - 2)}{5} = \frac{3 (n) + 3 (1)}{10}$

Factor $3$ out of $3 (n) + 3 (1)$ .

$\frac{2 (n - 2)}{5} = \frac{3 (n + 1)}{10}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$2 (n - 2) \cdot 10 = 5 (3 (n + 1))$

Step 3

Solve the equation for $n$ .

Simplify $2 (n - 2) \cdot 10$ .

Start simplifying.

$0 + 0 + 2 (n - 2) \cdot 10 = 5 \cdot (3 (n + 1))$

Simplify by adding zeros.

$2 (n - 2) \cdot 10 = 5 \cdot (3 (n + 1))$

Apply the distributive property.

$(2 n + 2 \cdot - 2) \cdot 10 = 5 \cdot (3 (n + 1))$

Multiply $2$ by $- 2$ .

$(2 n - 4) \cdot 10 = 5 \cdot (3 (n + 1))$

Apply the distributive property.

$2 n \cdot 10 - 4 \cdot 10 = 5 \cdot (3 (n + 1))$

Multiply.

Multiply $10$ by $2$ .

$20 n - 4 \cdot 10 = 5 \cdot (3 (n + 1))$

Multiply $- 4$ by $10$ .

$20 n - 40 = 5 \cdot (3 (n + 1))$

Simplify $5 \cdot (3 (n + 1))$ .

Apply the distributive property.

$20 n - 40 = 5 \cdot (3 n + 3 \cdot 1)$

Multiply $3$ by $1$ .

$20 n - 40 = 5 \cdot (3 n + 3)$

Apply the distributive property.

$20 n - 40 = 5 (3 n) + 5 \cdot 3$

Multiply.

Multiply $3$ by $5$ .

$20 n - 40 = 15 n + 5 \cdot 3$

Multiply $5$ by $3$ .

$20 n - 40 = 15 n + 15$

Move all terms containing $n$ to the left side of the equation.

Subtract $15 n$ from both sides of the equation.

$20 n - 40 - 15 n = 15$

Subtract $15 n$ from $20 n$ .

$5 n - 40 = 15$

Move all terms not containing $n$ to the right side of the equation.

Add $40$ to both sides of the equation.

$5 n = 15 + 40$

Add $15$ and $40$ .

$5 n = 55$

Divide each term in $5 n = 55$ by $5$ and simplify.

Divide each term in $5 n = 55$ by $5$ .

$\frac{5 n}{5} = \frac{55}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 n}{5} = \frac{55}{5}$

Divide $n$ by $1$ .

$n = \frac{55}{5}$

Simplify the right side.

Divide $55$ by $5$ .

$n = 11$

Solve for n (2n-4)/5=(3n+3)/10

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