(m-4)(m+2)=0

Solution for (m-4)(m+2)=0 equation:

Simplifying
(m + -4)(m + 2) = 0

Reorder the terms:
(-4 + m)(m + 2) = 0

Reorder the terms:
(-4 + m)(2 + m) = 0

Multiply (-4 + m) * (2 + m)
(-4(2 + m) + m(2 + m)) = 0
((2 * -4 + m * -4) + m(2 + m)) = 0
((-8 + -4m) + m(2 + m)) = 0
(-8 + -4m + (2 * m + m * m)) = 0
(-8 + -4m + (2m + m2)) = 0

Combine like terms: -4m + 2m = -2m
(-8 + -2m + m2) = 0

Solving
-8 + -2m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-2 + -1m)(4 + -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 '(4 + -1m)' equal to zero and attempt to solve:

Simplifying
4 + -1m = 0

Solving
4 + -1m = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1m = 0 + -4
-1m = 0 + -4

Combine like terms: 0 + -4 = -4
-1m = -4

Divide each side by '-1'.
m = 4

Simplifying
m = 4
Solution
m = {-2, 4}