Solve for v w=(15(t-2v))/v

$w = \frac{15 (t - 2 v)}{v}$

Step 1

Rewrite the equation as $\frac{15 (t - 2 v)}{v} = w$ .

$\frac{15 (t - 2 v)}{v} = w$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$v, 1$

The LCM of one and any expression is the expression.

$v$

Step 3

Multiply each term in $\frac{15 (t - 2 v)}{v} = w$ by $v$ to eliminate the fractions.

Multiply each term in $\frac{15 (t - 2 v)}{v} = w$ by $v$ .

$\frac{15 (t - 2 v)}{v} v = w v$

Simplify the left side.

Cancel the common factor of $v$ .

Cancel the common factor.

$\frac{15 (t - 2 v)}{v} v = w v$

Rewrite the expression.

$15 (t - 2 v) = w v$

Apply the distributive property.

$15 t + 15 (- 2 v) = w v$

Multiply $- 2$ by $15$ .

$15 t - 30 v = w v$

Step 4

Solve the equation.

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

$15 t - 30 v - w v = 0$

Subtract $15 t$ from both sides of the equation.

$- 30 v - w v = - 15 t$

Factor $v$ out of $- 30 v - w v$ .

Factor $v$ out of $- 30 v$ .

$v \cdot - 30 - w v = - 15 t$

Factor $v$ out of $- w v$ .

$v \cdot - 30 + v (- w) = - 15 t$

Factor $v$ out of $v \cdot - 30 + v (- w)$ .

$v (- 30 - w) = - 15 t$

Divide each term in $v (- 30 - w) = - 15 t$ by $- 30 - w$ and simplify.

Divide each term in $v (- 30 - w) = - 15 t$ by $- 30 - w$ .

$\frac{v (- 30 - w)}{- 30 - w} = \frac{- 15 t}{- 30 - w}$

Simplify the left side.

Cancel the common factor of $- 30 - w$ .

Cancel the common factor.

$\frac{v (- 30 - w)}{- 30 - w} = \frac{- 15 t}{- 30 - w}$

Divide $v$ by $1$ .

$v = \frac{- 15 t}{- 30 - w}$

Simplify the right side.

Move the negative in front of the fraction.

$v = - \frac{(15) t}{- 30 - w}$

Rewrite $- 30$ as $- 1 (30)$ .

$v = - \frac{15 t}{- 1 (30) - w}$

Factor $- 1$ out of $- w$ .

$v = - \frac{15 t}{- 1 (30) - (w)}$

Factor $- 1$ out of $- 1 (30) - (w)$ .

$v = - \frac{15 t}{- 1 (30 + w)}$

Simplify the expression.

Move the negative in front of the fraction.

$v = - - \frac{15 t}{30 + w}$

Multiply $- 1$ by $- 1$ .

$v = 1 \frac{15 t}{30 + w}$

Multiply $\frac{15 t}{30 + w}$ by $1$ .

$v = \frac{15 t}{30 + w}$

Solve for v w=(15(t-2v))/v

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