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

Solution for (6+m)(3-m)=0 equation:

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

Multiply (6 + m) * (3 + -1m)
(6(3 + -1m) + m(3 + -1m)) = 0
((3 * 6 + -1m * 6) + m(3 + -1m)) = 0
((18 + -6m) + m(3 + -1m)) = 0
(18 + -6m + (3 * m + -1m * m)) = 0
(18 + -6m + (3m + -1m2)) = 0

Combine like terms: -6m + 3m = -3m
(18 + -3m + -1m2) = 0

Solving
18 + -3m + -1m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(3 + -1m)(6 + m) = 0

Subproblem 1
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 0

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

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

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

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

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Subproblem 2
Set the factor '(6 + m)' equal to zero and attempt to solve:

Simplifying
6 + m = 0

Solving
6 + m = 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 + m = 0 + -6

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

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

Simplifying
m = -6
Solution
m = {3, -6}