Solve 4n+2mn=3mn ² for m.

m = sqrt (4 / (3 n) + 1 / (9 n^2)) + 1 / (3 n) or m = 1 / (3 n) - sqrt (4 / (3 n) + 1 / (9 n^2))

Step-by-step explanation:

Solve for m:

4 n + 2 m n = 3 m^2 n^2

Subtract 3 m^2 n^2 from both sides:

4 n + 2 m n - 3 m^2 n^2 = 0

Divide both sides by - 3 n^2:

m^2 - 4 / (3 n) - (2 m) / (3 n) = 0

Add 4 / (3 n) to both sides:

m^2 - (2 m) / (3 n) = 4 / (3 n)

Add 1 / (9 n^2) to both sides:

m^2 + 1 / (9 n^2) - (2 m) / (3 n) = 4 / (3 n) + 1 / (9 n^2)

Write the left hand side as a square:

(m - 1 / (3 n)) ^2 = 4 / (3 n) + 1 / (9 n^2)

Take the square root of both sides:

m - 1 / (3 n) = sqrt (4 / (3 n) + 1 / (9 n^2)) or m - 1 / (3 n) = - sqrt (4 / (3 n) + 1 / (9 n^2))

Add 1 / (3 n) to both sides:

m = sqrt (4 / (3 n) + 1 / (9 n^2)) + 1 / (3 n) or m - 1 / (3 n) = - sqrt (4 / (3 n) + 1 / (9 n^2))

Add 1 / (3 n) to both sides:

Answer: m = sqrt (4 / (3 n) + 1 / (9 n^2)) + 1 / (3 n) or m = 1 / (3 n) - sqrt (4 / (3 n) + 1 / (9 n^2))