(4m+3n)(4m-3n)=0

Solution for (4m+3n)(4m-3n)=0 equation:

Simplifying
(4m + 3n)(4m + -3n) = 0

Multiply (4m + 3n) * (4m + -3n)
(4m * (4m + -3n) + 3n * (4m + -3n)) = 0
((4m * 4m + -3n * 4m) + 3n * (4m + -3n)) = 0

Reorder the terms:
((-12mn + 16m2) + 3n * (4m + -3n)) = 0
((-12mn + 16m2) + 3n * (4m + -3n)) = 0
(-12mn + 16m2 + (4m * 3n + -3n * 3n)) = 0
(-12mn + 16m2 + (12mn + -9n2)) = 0

Reorder the terms:
(-12mn + 12mn + 16m2 + -9n2) = 0

Combine like terms: -12mn + 12mn = 0
(0 + 16m2 + -9n2) = 0
(16m2 + -9n2) = 0

Solving
16m2 + -9n2 = 0

Solving for variable 'm'.

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

Add '9n2' to each side of the equation.
16m2 + -9n2 + 9n2 = 0 + 9n2

Combine like terms: -9n2 + 9n2 = 0
16m2 + 0 = 0 + 9n2
16m2 = 0 + 9n2
Remove the zero:
16m2 = 9n2

Divide each side by '16'.
m2 = 0.5625n2

Simplifying
m2 = 0.5625n2

Take the square root of each side:
m = {-0.75n, 0.75n}