Solve for n 7(1+4n)=7(6+3n)

$7 (1 + 4 n) = 7 (6 + 3 n)$

Simplify $7 (1 + 4 n)$ .

Start simplifying.

$0 + 0 + 7 (1 + 4 n) = 7 (6 + 3 n)$

Simplify by adding zeros.

$7 (1 + 4 n) = 7 (6 + 3 n)$

Apply the distributive property.

$7 \cdot 1 + 7 (4 n) = 7 (6 + 3 n)$

Multiply.

Multiply $7$ by $1$ .

$7 + 7 (4 n) = 7 (6 + 3 n)$

Multiply $4$ by $7$ .

$7 + 28 n = 7 (6 + 3 n)$

Simplify $7 (6 + 3 n)$ .

Apply the distributive property.

$7 + 28 n = 7 \cdot 6 + 7 (3 n)$

Multiply.

Multiply $7$ by $6$ .

$7 + 28 n = 42 + 7 (3 n)$

Multiply $3$ by $7$ .

$7 + 28 n = 42 + 21 n$

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

Subtract $21 n$ from both sides of the equation.

$7 + 28 n - 21 n = 42$

Subtract $21 n$ from $28 n$ .

$7 + 7 n = 42$

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

Subtract $7$ from both sides of the equation.

$7 n = 42 - 7$

Subtract $7$ from $42$ .

$7 n = 35$

Divide each term in $7 n = 35$ by $7$ and simplify.

Divide each term in $7 n = 35$ by $7$ .

$\frac{7 n}{7} = \frac{35}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 n}{7} = \frac{35}{7}$

Divide $n$ by $1$ .

$n = \frac{35}{7}$

Simplify the right side.

Divide $35$ by $7$ .

$n = 5$