m+2n+(2)(3n)=2(m+n)

Solution for m+2n+(2)(3n)=2(m+n) equation:

Simplifying
m + 2n + (2)(3n) = 2(m + n)

Remove parenthesis around (3n)
m + 2n + 2 * 3n = 2(m + n)

Multiply 2 * 3
m + 2n + 6n = 2(m + n)

Combine like terms: 2n + 6n = 8n
m + 8n = 2(m + n)
m + 8n = (m * 2 + n * 2)
m + 8n = (2m + 2n)

Solving
m + 8n = 2m + 2n

Solving for variable 'm'.

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

Add '-2m' to each side of the equation.
m + -2m + 8n = 2m + -2m + 2n

Combine like terms: m + -2m = -1m
-1m + 8n = 2m + -2m + 2n

Combine like terms: 2m + -2m = 0
-1m + 8n = 0 + 2n
-1m + 8n = 2n

Add '-8n' to each side of the equation.
-1m + 8n + -8n = 2n + -8n

Combine like terms: 8n + -8n = 0
-1m + 0 = 2n + -8n
-1m = 2n + -8n

Combine like terms: 2n + -8n = -6n
-1m = -6n

Divide each side by '-1'.
m = 6n

Simplifying
m = 6n