7m^2-18mn+8n^2=0

Solution for 7m^2-18mn+8n^2=0 equation:

Simplifying
7m2 + -18mn + 8n2 = 0

Reorder the terms:
-18mn + 7m2 + 8n2 = 0

Solving
-18mn + 7m2 + 8n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -2n)(7m + -4n) = 0

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

Simplifying
m + -2n = 0

Solving
m + -2n = 0

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

Add '2n' to each side of the equation.
m + -2n + 2n = 0 + 2n

Combine like terms: -2n + 2n = 0
m + 0 = 0 + 2n
m = 0 + 2n
Remove the zero:
m = 2n

Simplifying
m = 2n
Subproblem 2
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
Solution
m = {2n, 0.5714285714n}