(x-4)(m+2n)+n(x-4)=0

Solution for (x-4)(m+2n)+n(x-4)=0 equation:

Simplifying
(x + -4)(m + 2n) + n(x + -4) = 0

Reorder the terms:
(-4 + x)(m + 2n) + n(x + -4) = 0

Multiply (-4 + x) * (m + 2n)
(-4(m + 2n) + x(m + 2n)) + n(x + -4) = 0
((m * -4 + 2n * -4) + x(m + 2n)) + n(x + -4) = 0
((-4m + -8n) + x(m + 2n)) + n(x + -4) = 0
(-4m + -8n + (m * x + 2n * x)) + n(x + -4) = 0
(-4m + -8n + (mx + 2nx)) + n(x + -4) = 0

Reorder the terms:
(-4m + mx + -8n + 2nx) + n(x + -4) = 0
(-4m + mx + -8n + 2nx) + n(x + -4) = 0

Reorder the terms:
-4m + mx + -8n + 2nx + n(-4 + x) = 0
-4m + mx + -8n + 2nx + (-4 * n + x * n) = 0
-4m + mx + -8n + 2nx + (-4n + nx) = 0

Reorder the terms:
-4m + mx + -8n + -4n + 2nx + nx = 0

Combine like terms: -8n + -4n = -12n
-4m + mx + -12n + 2nx + nx = 0

Combine like terms: 2nx + nx = 3nx
-4m + mx + -12n + 3nx = 0

Solving
-4m + mx + -12n + 3nx = 0

Solving for variable 'm'.

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

Add '12n' to each side of the equation.
-4m + mx + -12n + 12n + 3nx = 0 + 12n

Combine like terms: -12n + 12n = 0
-4m + mx + 0 + 3nx = 0 + 12n
-4m + mx + 3nx = 0 + 12n
Remove the zero:
-4m + mx + 3nx = 12n

Add '-3nx' to each side of the equation.
-4m + mx + 3nx + -3nx = 12n + -3nx

Combine like terms: 3nx + -3nx = 0
-4m + mx + 0 = 12n + -3nx
-4m + mx = 12n + -3nx

Reorder the terms:
-4m + mx + -12n + 3nx = 12n + -12n + -3nx + 3nx

Combine like terms: 12n + -12n = 0
-4m + mx + -12n + 3nx = 0 + -3nx + 3nx
-4m + mx + -12n + 3nx = -3nx + 3nx

Combine like terms: -3nx + 3nx = 0
-4m + mx + -12n + 3nx = 0

The solution to this equation could not be determined.