3(m+2)-m(m-2)=0

Solution for 3(m+2)-m(m-2)=0 equation:

Simplifying
3(m + 2) + -1m(m + -2) = 0

Reorder the terms:
3(2 + m) + -1m(m + -2) = 0
(2 * 3 + m * 3) + -1m(m + -2) = 0
(6 + 3m) + -1m(m + -2) = 0

Reorder the terms:
6 + 3m + -1m(-2 + m) = 0
6 + 3m + (-2 * -1m + m * -1m) = 0
6 + 3m + (2m + -1m2) = 0

Combine like terms: 3m + 2m = 5m
6 + 5m + -1m2 = 0

Solving
6 + 5m + -1m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(6 + -1m)(1 + m) = 0

Subproblem 1
Set the factor '(6 + -1m)' equal to zero and attempt to solve:

Simplifying
6 + -1m = 0

Solving
6 + -1m = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1m = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1m = 0 + -6
-1m = 0 + -6

Combine like terms: 0 + -6 = -6
-1m = -6

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

Simplifying
m = 6
Subproblem 2
Set the factor '(1 + m)' equal to zero and attempt to solve:

Simplifying
1 + m = 0

Solving
1 + m = 0

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

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

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

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

Simplifying
m = -1
Solution
m = {6, -1}