x^2+(m-n)x+2(m-n)=0

Solution for x^2+(m-n)x+2(m-n)=0 equation:

Simplifying
x2 + (m + -1n) * x + 2(m + -1n) = 0

Reorder the terms for easier multiplication:
x2 + x(m + -1n) + 2(m + -1n) = 0
x2 + (m * x + -1n * x) + 2(m + -1n) = 0
x2 + (mx + -1nx) + 2(m + -1n) = 0
x2 + mx + -1nx + (m * 2 + -1n * 2) = 0
x2 + mx + -1nx + (2m + -2n) = 0

Reorder the terms:
2m + mx + -2n + -1nx + x2 = 0

Solving
2m + mx + -2n + -1nx + x2 = 0

Solving for variable 'm'.

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

Add '2n' to each side of the equation.
2m + mx + -2n + -1nx + 2n + x2 = 0 + 2n

Reorder the terms:
2m + mx + -2n + 2n + -1nx + x2 = 0 + 2n

Combine like terms: -2n + 2n = 0
2m + mx + 0 + -1nx + x2 = 0 + 2n
2m + mx + -1nx + x2 = 0 + 2n
Remove the zero:
2m + mx + -1nx + x2 = 2n

Add 'nx' to each side of the equation.
2m + mx + -1nx + nx + x2 = 2n + nx

Combine like terms: -1nx + nx = 0
2m + mx + 0 + x2 = 2n + nx
2m + mx + x2 = 2n + nx

Add '-1x2' to each side of the equation.
2m + mx + x2 + -1x2 = 2n + nx + -1x2

Combine like terms: x2 + -1x2 = 0
2m + mx + 0 = 2n + nx + -1x2
2m + mx = 2n + nx + -1x2

Reorder the terms:
2m + mx + -2n + -1nx + x2 = 2n + -2n + nx + -1nx + -1x2 + x2

Combine like terms: 2n + -2n = 0
2m + mx + -2n + -1nx + x2 = 0 + nx + -1nx + -1x2 + x2
2m + mx + -2n + -1nx + x2 = nx + -1nx + -1x2 + x2

Combine like terms: nx + -1nx = 0
2m + mx + -2n + -1nx + x2 = 0 + -1x2 + x2
2m + mx + -2n + -1nx + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
2m + mx + -2n + -1nx + x2 = 0

The solution to this equation could not be determined.