Solve for n 6(5n-6)-10=10-3n+10

$6 (5 n - 6) - 10 = 10 - 3 n + 10$

Simplify $6 (5 n - 6) - 10$ .

Simplify each term.

Apply the distributive property.

$6 (5 n) + 6 \cdot - 6 - 10 = 10 - 3 n + 10$

Multiply $5$ by $6$ .

$30 n + 6 \cdot - 6 - 10 = 10 - 3 n + 10$

Multiply $6$ by $- 6$ .

$30 n - 36 - 10 = 10 - 3 n + 10$

Subtract $10$ from $- 36$ .

$30 n - 46 = 10 - 3 n + 10$

Add $10$ and $10$ .

$30 n - 46 = - 3 n + 20$

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

Add $3 n$ to both sides of the equation.

$30 n - 46 + 3 n = 20$

Add $30 n$ and $3 n$ .

$33 n - 46 = 20$

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

Add $46$ to both sides of the equation.

$33 n = 20 + 46$

Add $20$ and $46$ .

$33 n = 66$

Divide each term in $33 n = 66$ by $33$ and simplify.

Divide each term in $33 n = 66$ by $33$ .

$\frac{33 n}{33} = \frac{66}{33}$

Simplify the left side.

Cancel the common factor of $33$ .

Cancel the common factor.

$\frac{33 n}{33} = \frac{66}{33}$

Divide $n$ by $1$ .

$n = \frac{66}{33}$

Simplify the right side.

Divide $66$ by $33$ .

$n = 2$