Solve for v 7(2+5v)=3v+14

$7 (2 + 5 v) = 3 v + 14$

Step 1

Simplify $7 (2 + 5 v)$ .

Rewrite.

$0 + 0 + 7 (2 + 5 v) = 3 v + 14$

Simplify by adding zeros.

$7 (2 + 5 v) = 3 v + 14$

Apply the distributive property.

$7 \cdot 2 + 7 (5 v) = 3 v + 14$

Multiply.

Multiply $7$ by $2$ .

$14 + 7 (5 v) = 3 v + 14$

Multiply $5$ by $7$ .

$14 + 35 v = 3 v + 14$

Step 2

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

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

$14 + 35 v - 3 v = 14$

Subtract $3 v$ from $35 v$ .

$14 + 32 v = 14$

Step 3

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

Subtract $14$ from both sides of the equation.

$32 v = 14 - 14$

Subtract $14$ from $14$ .

$32 v = 0$

Step 4

Divide each term in $32 v = 0$ by $32$ and simplify.

Divide each term in $32 v = 0$ by $32$ .

$\frac{32 v}{32} = \frac{0}{32}$

Simplify the left side.

Cancel the common factor of $32$ .

Cancel the common factor.

$\frac{32 v}{32} = \frac{0}{32}$

Divide $v$ by $1$ .

$v = \frac{0}{32}$

Simplify the right side.

Divide $0$ by $32$ .

$v = 0$