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

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

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

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

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

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

Combine like terms: -2m + 3m = 1m
2(-6 + 1m + m2) = 0
(-6 * 2 + 1m * 2 + m2 * 2) = 0
(-12 + 2m + 2m2) = 0

Solving
-12 + 2m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + m + m2) = 0

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

Ignore the factor 2.
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 '(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
Solution
m = {-3, 2}