6m(m+3n+1)=

Solution for 6m(m+3n+1)= equation:

Simplifying
6m(m + 3n + 1) = 0

Reorder the terms:
6m(1 + m + 3n) = 0
(1 * 6m + m * 6m + 3n * 6m) = 0

Reorder the terms:
(6m + 18mn + 6m2) = 0
(6m + 18mn + 6m2) = 0

Solving
6m + 18mn + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '6m'.
6m(1 + 3n + m) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
Set the factor '(1 + 3n + m)' equal to zero and attempt to solve:

Simplifying
1 + 3n + m = 0

Reorder the terms:
1 + m + 3n = 0

Solving
1 + m + 3n = 0

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

Add '-1' to each side of the equation.
1 + m + -1 + 3n = 0 + -1

Reorder the terms:
1 + -1 + m + 3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + m + 3n = 0 + -1
m + 3n = 0 + -1

Combine like terms: 0 + -1 = -1
m + 3n = -1

Add '-3n' to each side of the equation.
m + 3n + -3n = -1 + -3n

Combine like terms: 3n + -3n = 0
m + 0 = -1 + -3n
m = -1 + -3n

Simplifying
m = -1 + -3n
Solution
m = {0, -1 + -3n}