16*m^4-25*m^2*n^2+9*n^4=0

Solution for 16*m^4-25*m^2*n^2+9*n^4=0 equation:

Simplifying
16m4 + -25m2 * n2 + 9n4 = 0

Multiply m2 * n2
16m4 + -25m2n2 + 9n4 = 0

Reorder the terms:
-25m2n2 + 16m4 + 9n4 = 0

Solving
-25m2n2 + 16m4 + 9n4 = 0

Solving for variable 'm'.

Factor a trinomial.
(m2 + -1n2)(16m2 + -9n2) = 0

Factor a difference between two squares.
((m + n)(m + -1n))(16m2 + -9n2) = 0

Factor a difference between two squares.
((4m + 3n)(4m + -3n))(m + n)(m + -1n) = 0

Subproblem 1
Set the factor '(m + n)' equal to zero and attempt to solve:

Simplifying
m + n = 0

Solving
m + n = 0

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

Add '-1n' to each side of the equation.
m + n + -1n = 0 + -1n

Combine like terms: n + -1n = 0
m + 0 = 0 + -1n
m = 0 + -1n
Remove the zero:
m = -1n

Simplifying
m = -1n
Subproblem 2
Set the factor '(m + -1n)' equal to zero and attempt to solve:

Simplifying
m + -1n = 0

Solving
m + -1n = 0

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

Add 'n' to each side of the equation.
m + -1n + n = 0 + n

Combine like terms: -1n + n = 0
m + 0 = 0 + n
m = 0 + n
Remove the zero:
m = n

Simplifying
m = n
Subproblem 3
Set the factor '(4m + 3n)' equal to zero and attempt to solve:

Simplifying
4m + 3n = 0

Solving
4m + 3n = 0

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

Add '-3n' to each side of the equation.
4m + 3n + -3n = 0 + -3n

Combine like terms: 3n + -3n = 0
4m + 0 = 0 + -3n
4m = 0 + -3n
Remove the zero:
4m = -3n

Divide each side by '4'.
m = -0.75n

Simplifying
m = -0.75n
Subproblem 4
Set the factor '(4m + -3n)' equal to zero and attempt to solve:

Simplifying
4m + -3n = 0

Solving
4m + -3n = 0

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

Add '3n' to each side of the equation.
4m + -3n + 3n = 0 + 3n

Combine like terms: -3n + 3n = 0
4m + 0 = 0 + 3n
4m = 0 + 3n
Remove the zero:
4m = 3n

Divide each side by '4'.
m = 0.75n

Simplifying
m = 0.75n
Solution
m = {-1n, n, -0.75n, 0.75n}