Solve for n 3(2n+1)=4n+9

$3 (2 n + 1) = 4 n + 9$

Step 1

Simplify $3 (2 n + 1)$ .

Rewrite.

$0 + 0 + 3 (2 n + 1) = 4 n + 9$

Simplify by adding zeros.

$3 (2 n + 1) = 4 n + 9$

Apply the distributive property.

$3 (2 n) + 3 \cdot 1 = 4 n + 9$

Multiply.

Multiply $2$ by $3$ .

$6 n + 3 \cdot 1 = 4 n + 9$

Multiply $3$ by $1$ .

$6 n + 3 = 4 n + 9$

Step 2

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

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

$6 n + 3 - 4 n = 9$

Subtract $4 n$ from $6 n$ .

$2 n + 3 = 9$

Step 3

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

Subtract $3$ from both sides of the equation.

$2 n = 9 - 3$

Subtract $3$ from $9$ .

$2 n = 6$

Step 4

Divide each term in $2 n = 6$ by $2$ and simplify.

Divide each term in $2 n = 6$ by $2$ .

$\frac{2 n}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} = \frac{6}{2}$

Divide $n$ by $1$ .

$n = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$n = 3$