Solve for v2 ((v_1-v_2)w)/6=s

$\frac{(v_{1} - v_{2}) w}{6} = s$

Multiply both sides by $6$ .

$\frac{(v_{1} - v_{2}) w}{6} \cdot 6 = s \cdot 6$

Simplify.

Simplify the left side.

Simplify $\frac{(v_{1} - v_{2}) w}{6} \cdot 6$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{(v_{1} - v_{2}) w}{6} \cdot 6 = s \cdot 6$

Rewrite the expression.

$(v_{1} - v_{2}) w = s \cdot 6$

Apply the distributive property.

$v_{1} w - v_{2} w = s \cdot 6$

Simplify the expression.

Reorder $v_{1}$ and $w$ .

$w v_{1} - v_{2} w = s \cdot 6$

Move $v_{2}$ .

$w v_{1} - 1 w v_{2} = s \cdot 6$

Simplify the right side.

Move $6$ to the left of $s$ .

$w v_{1} - 1 w v_{2} = 6 s$

Solve for $v_{1}$ .

Rewrite $- 1 w$ as $- w$ .

$w v_{1} - w v_{2} = 6 s$

Add $w v_{2}$ to both sides of the equation.

$w v_{1} = 6 s + w v_{2}$

Divide each term in $w v_{1} = 6 s + w v_{2}$ by $w$ and simplify.

Divide each term in $w v_{1} = 6 s + w v_{2}$ by $w$ .

$\frac{w v_{1}}{w} = \frac{6 s}{w} + \frac{w v_{2}}{w}$

Simplify the left side.

Cancel the common factor of $w$ .

Cancel the common factor.

$\frac{w v_{1}}{w} = \frac{6 s}{w} + \frac{w v_{2}}{w}$

Divide $v_{1}$ by $1$ .

$v_{1} = \frac{6 s}{w} + \frac{w v_{2}}{w}$

Simplify the right side.

Cancel the common factor of $w$ .

Cancel the common factor.

$v_{1} = \frac{6 s}{w} + \frac{w v_{2}}{w}$

Divide $v_{2}$ by $1$ .

$v_{1} = \frac{6 s}{w} + v_{2}$