(m-4)(m+6)=0

Solution for (m-4)(m+6)=0 equation:

Simplifying
(m + -4)(m + 6) = 0

Reorder the terms:
(-4 + m)(m + 6) = 0

Reorder the terms:
(-4 + m)(6 + m) = 0

Multiply (-4 + m) * (6 + m)
(-4(6 + m) + m(6 + m)) = 0
((6 * -4 + m * -4) + m(6 + m)) = 0
((-24 + -4m) + m(6 + m)) = 0
(-24 + -4m + (6 * m + m * m)) = 0
(-24 + -4m + (6m + m2)) = 0

Combine like terms: -4m + 6m = 2m
(-24 + 2m + m2) = 0

Solving
-24 + 2m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-6 + -1m)(4 + -1m) = 0

Subproblem 1
Set the factor '(-6 + -1m)' equal to zero and attempt to solve:

Simplifying
-6 + -1m = 0

Solving
-6 + -1m = 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 + -1m = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1m = 0 + 6
-1m = 0 + 6

Combine like terms: 0 + 6 = 6
-1m = 6

Divide each side by '-1'.
m = -6

Simplifying
m = -6
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 = {-6, 4}