Solve for v 3/5v=2/3(4/5v-6)

$\frac{3}{5} v = \frac{2}{3} (\frac{4}{5} v - 6)$

Simplify $\frac{3}{5} v$ .

Start simplifying.

$0 + 0 + \frac{3}{5} v = \frac{2}{3} \cdot (\frac{4}{5} v - 6)$

Simplify by adding zeros.

$\frac{3}{5} v = \frac{2}{3} \cdot (\frac{4}{5} v - 6)$

Combine $\frac{3}{5}$ and $v$ .

$\frac{3 v}{5} = \frac{2}{3} \cdot (\frac{4}{5} v - 6)$

Simplify $\frac{2}{3} \cdot (\frac{4}{5} v - 6)$ .

Combine $\frac{4}{5}$ and $v$ .

$\frac{3 v}{5} = \frac{2}{3} \cdot (\frac{4 v}{5} - 6)$

Apply the distributive property.

$\frac{3 v}{5} = \frac{2}{3} \cdot \frac{4 v}{5} + \frac{2}{3} \cdot - 6$

Multiply $\frac{2}{3} \cdot \frac{4 v}{5}$ .

Multiply $\frac{2}{3}$ by $\frac{4 v}{5}$ .

$\frac{3 v}{5} = \frac{2 (4 v)}{3 \cdot 5} + \frac{2}{3} \cdot - 6$

Multiply $4$ by $2$ .

$\frac{3 v}{5} = \frac{8 v}{3 \cdot 5} + \frac{2}{3} \cdot - 6$

Multiply $3$ by $5$ .

$\frac{3 v}{5} = \frac{8 v}{15} + \frac{2}{3} \cdot - 6$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$\frac{3 v}{5} = \frac{8 v}{15} + \frac{2}{3} \cdot (3 (- 2))$

Cancel the common factor.

$\frac{3 v}{5} = \frac{8 v}{15} + \frac{2}{3} \cdot (3 \cdot - 2)$

Rewrite the expression.

$\frac{3 v}{5} = \frac{8 v}{15} + 2 \cdot - 2$

Multiply $2$ by $- 2$ .

$\frac{3 v}{5} = \frac{8 v}{15} - 4$

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

Subtract $\frac{8 v}{15}$ from both sides of the equation.

$\frac{3 v}{5} - \frac{8 v}{15} = - 4$

To write $\frac{3 v}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 v}{5} \cdot \frac{3}{3} - \frac{8 v}{15} = - 4$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 v}{5}$ by $\frac{3}{3}$ .

$\frac{3 v \cdot 3}{5 \cdot 3} - \frac{8 v}{15} = - 4$

Multiply $5$ by $3$ .

$\frac{3 v \cdot 3}{15} - \frac{8 v}{15} = - 4$

Combine the numerators over the common denominator.

$\frac{3 v \cdot 3 - 8 v}{15} = - 4$

Simplify the numerator.

Factor $v$ out of $3 v \cdot 3 - 8 v$ .

Factor $v$ out of $3 v \cdot 3$ .

$\frac{v (3 \cdot 3) - 8 v}{15} = - 4$

Factor $v$ out of $- 8 v$ .

$\frac{v (3 \cdot 3) + v \cdot - 8}{15} = - 4$

Factor $v$ out of $v (3 \cdot 3) + v \cdot - 8$ .

$\frac{v (3 \cdot 3 - 8)}{15} = - 4$

Multiply $3$ by $3$ .

$\frac{v (9 - 8)}{15} = - 4$

Subtract $8$ from $9$ .

$\frac{v \cdot 1}{15} = - 4$

Multiply $v$ by $1$ .

$\frac{v}{15} = - 4$

Multiply both sides of the equation by $15$ .

$15 \frac{v}{15} = 15 \cdot - 4$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$15 \frac{v}{15} = 15 \cdot - 4$

Rewrite the expression.

$v = 15 \cdot - 4$

Simplify the right side.

Multiply $15$ by $- 4$ .

$v = - 60$

Solve for v 3/5v=2/3(4/5v-6)

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