7m^2+45mn-28n^2=0

Solution for 7m^2+45mn-28n^2=0 equation:

Simplifying
7m2 + 45mn + -28n2 = 0

Reorder the terms:
45mn + 7m2 + -28n2 = 0

Solving
45mn + 7m2 + -28n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(7m + -4n)(m + 7n) = 0

Subproblem 1
Set the factor '(7m + -4n)' equal to zero and attempt to solve:

Simplifying
7m + -4n = 0

Solving
7m + -4n = 0

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

Add '4n' to each side of the equation.
7m + -4n + 4n = 0 + 4n

Combine like terms: -4n + 4n = 0
7m + 0 = 0 + 4n
7m = 0 + 4n
Remove the zero:
7m = 4n

Divide each side by '7'.
m = 0.5714285714n

Simplifying
m = 0.5714285714n
Subproblem 2
Set the factor '(m + 7n)' equal to zero and attempt to solve:

Simplifying
m + 7n = 0

Solving
m + 7n = 0

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

Add '-7n' to each side of the equation.
m + 7n + -7n = 0 + -7n

Combine like terms: 7n + -7n = 0
m + 0 = 0 + -7n
m = 0 + -7n
Remove the zero:
m = -7n

Simplifying
m = -7n
Solution
m = {0.5714285714n, -7n}