Solve for n 3(n+4)=1/2(6n+4)

$3 (n + 4) = \frac{1}{2} (6 n + 4)$

Step 1

Simplify $3 (n + 4)$ .

Rewrite.

$0 + 0 + 3 (n + 4) = \frac{1}{2} \cdot (6 n + 4)$

Simplify by adding zeros.

$3 (n + 4) = \frac{1}{2} \cdot (6 n + 4)$

Apply the distributive property.

$3 n + 3 \cdot 4 = \frac{1}{2} \cdot (6 n + 4)$

Multiply $3$ by $4$ .

$3 n + 12 = \frac{1}{2} \cdot (6 n + 4)$

Step 2

Simplify $\frac{1}{2} \cdot (6 n + 4)$ .

Apply the distributive property.

$3 n + 12 = \frac{1}{2} (6 n) + \frac{1}{2} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $6 n$ .

$3 n + 12 = \frac{1}{2} (2 (3 n)) + \frac{1}{2} \cdot 4$

Cancel the common factor.

$3 n + 12 = \frac{1}{2} (2 (3 n)) + \frac{1}{2} \cdot 4$

Rewrite the expression.

$3 n + 12 = 3 n + \frac{1}{2} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$3 n + 12 = 3 n + \frac{1}{2} \cdot (2 (2))$

Cancel the common factor.

$3 n + 12 = 3 n + \frac{1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$3 n + 12 = 3 n + 2$

Step 3

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

Subtract $3 n$ from both sides of the equation.

$3 n + 12 - 3 n = 2$

Combine the opposite terms in $3 n + 12 - 3 n$ .

Subtract $3 n$ from $3 n$ .

$0 + 12 = 2$

Add $0$ and $12$ .

$12 = 2$

Step 4

Since $12 \neq 2$ , there are no solutions.

No solution