Solve for n 6-(8-4n)=2(2n-1)

$6 - (8 - 4 n) = 2 (2 n - 1)$

Simplify $6 - (8 - 4 n)$ .

Simplify each term.

Apply the distributive property.

$6 - 1 \cdot 8 - (- 4 n) = 2 (2 n - 1)$

Multiply $- 1$ by $8$ .

$6 - 8 - (- 4 n) = 2 (2 n - 1)$

Multiply $- 4$ by $- 1$ .

$6 - 8 + 4 n = 2 (2 n - 1)$

Subtract $8$ from $6$ .

$- 2 + 4 n = 2 (2 n - 1)$

Simplify $2 (2 n - 1)$ .

Apply the distributive property.

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

Multiply.

Multiply $2$ by $2$ .

$- 2 + 4 n = 4 n + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$- 2 + 4 n = 4 n - 2$

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

Subtract $4 n$ from both sides of the equation.

$- 2 + 4 n - 4 n = - 2$

Combine the opposite terms in $- 2 + 4 n - 4 n$ .

Subtract $4 n$ from $4 n$ .

$- 2 + 0 = - 2$

Add $- 2$ and $0$ .

$- 2 = - 2$

Since $- 2 = - 2$ , the equation will always be true for any value of $n$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$