Solve for m v^2=(3P)/(mn)

$v^{2} = \frac{3 P}{m n}$

Rewrite the equation as $\frac{3 P}{m n} = v^{2}$ .

$\frac{3 P}{m n} = v^{2}$

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.

$m n, 1$

The LCM of one and any expression is the expression.

$m n$

Multiply each term in $\frac{3 P}{m n} = v^{2}$ by $m n$ to eliminate the fractions.

Multiply each term in $\frac{3 P}{m n} = v^{2}$ by $m n$ .

$\frac{3 P}{m n} (m n) = v^{2} (m n)$

Simplify the left side.

Cancel the common factor of $m n$ .

Cancel the common factor.

$\frac{3 P}{m n} (m n) = v^{2} (m n)$

Rewrite the expression.

$3 P = v^{2} (m n)$

Simplify the right side.

Remove parentheses.

$3 P = v^{2} m n$

Solve the equation.

Rewrite the equation as $v^{2} m n = 3 P$ .

$v^{2} m n = 3 P$

Divide each term in $v^{2} m n = 3 P$ by $v^{2} n$ and simplify.

Divide each term in $v^{2} m n = 3 P$ by $v^{2} n$ .

$\frac{v^{2} m n}{v^{2} n} = \frac{3 P}{v^{2} n}$

Simplify the left side.

Cancel the common factor of $v^{2}$ .

Cancel the common factor.

$\frac{v^{2} m n}{v^{2} n} = \frac{3 P}{v^{2} n}$

Rewrite the expression.

$\frac{m n}{n} = \frac{3 P}{v^{2} n}$

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{m n}{n} = \frac{3 P}{v^{2} n}$

Divide $m$ by $1$ .

$m = \frac{3 P}{v^{2} n}$