(3m+n)(3m-n)=

Solution for (3m+n)(3m-n)= equation:

Simplifying
(3m + n)(3m + -1n) = 0

Multiply (3m + n) * (3m + -1n)
(3m * (3m + -1n) + n(3m + -1n)) = 0
((3m * 3m + -1n * 3m) + n(3m + -1n)) = 0

Reorder the terms:
((-3mn + 9m2) + n(3m + -1n)) = 0
((-3mn + 9m2) + n(3m + -1n)) = 0
(-3mn + 9m2 + (3m * n + -1n * n)) = 0
(-3mn + 9m2 + (3mn + -1n2)) = 0

Reorder the terms:
(-3mn + 3mn + 9m2 + -1n2) = 0

Combine like terms: -3mn + 3mn = 0
(0 + 9m2 + -1n2) = 0
(9m2 + -1n2) = 0

Solving
9m2 + -1n2 = 0

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add 'n2' to each side of the equation.
9m2 + -1n2 + n2 = 0 + n2

Combine like terms: -1n2 + n2 = 0
9m2 + 0 = 0 + n2
9m2 = 0 + n2
Remove the zero:
9m2 = n2

Divide each side by '9'.
m2 = 0.1111111111n2

Simplifying
m2 = 0.1111111111n2

Take the square root of each side:
m = {-0.333333333n, 0.333333333n}