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

Solution for (5-m)(m+2)=0 equation:

Simplifying
(5 + -1m)(m + 2) = 0

Reorder the terms:
(5 + -1m)(2 + m) = 0

Multiply (5 + -1m) * (2 + m)
(5(2 + m) + -1m * (2 + m)) = 0
((2 * 5 + m * 5) + -1m * (2 + m)) = 0
((10 + 5m) + -1m * (2 + m)) = 0
(10 + 5m + (2 * -1m + m * -1m)) = 0
(10 + 5m + (-2m + -1m2)) = 0

Combine like terms: 5m + -2m = 3m
(10 + 3m + -1m2) = 0

Solving
10 + 3m + -1m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(5 + -1m)(2 + m) = 0

Subproblem 1
Set the factor '(5 + -1m)' equal to zero and attempt to solve:

Simplifying
5 + -1m = 0

Solving
5 + -1m = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1m = 0 + -5
-1m = 0 + -5

Combine like terms: 0 + -5 = -5
-1m = -5

Divide each side by '-1'.
m = 5

Simplifying
m = 5
Subproblem 2
Set the factor '(2 + m)' equal to zero and attempt to solve:

Simplifying
2 + m = 0

Solving
2 + m = 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 + m = 0 + -2

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

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

Simplifying
m = -2
Solution
m = {5, -2}