(m+2)(2m-6)=0

Solution for (m+2)(2m-6)=0 equation:

Simplifying
(m + 2)(2m + -6) = 0

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

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

Multiply (2 + m) * (-6 + 2m)
(2(-6 + 2m) + m(-6 + 2m)) = 0
((-6 * 2 + 2m * 2) + m(-6 + 2m)) = 0
((-12 + 4m) + m(-6 + 2m)) = 0
(-12 + 4m + (-6 * m + 2m * m)) = 0
(-12 + 4m + (-6m + 2m2)) = 0

Combine like terms: 4m + -6m = -2m
(-12 + -2m + 2m2) = 0

Solving
-12 + -2m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1m + m2) = 0

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

Ignore the factor 2.
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}