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

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

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

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

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

Multiply (-3 + m) * (2 + m)
(-3(2 + m) + m(2 + m)) = 0
((2 * -3 + m * -3) + m(2 + m)) = 0
((-6 + -3m) + m(2 + m)) = 0
(-6 + -3m + (2 * m + m * m)) = 0
(-6 + -3m + (2m + m2)) = 0

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

Solving
-6 + -1m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-2 + -1m)(3 + -1m) = 0

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

Simplifying
-2 + -1m = 0

Solving
-2 + -1m = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1m = 0 + 2

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

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

Divide each side by '-1'.
m = -2

Simplifying
m = -2
Subproblem 2
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
Solution
m = {-2, 3}