(m-3)(m+5)=0

Solution for (m-3)(m+5)=0 equation:

Simplifying
(m + -3)(m + 5) = 0

Reorder the terms:
(-3 + m)(m + 5) = 0

Reorder the terms:
(-3 + m)(5 + m) = 0

Multiply (-3 + m) * (5 + m)
(-3(5 + m) + m(5 + m)) = 0
((5 * -3 + m * -3) + m(5 + m)) = 0
((-15 + -3m) + m(5 + m)) = 0
(-15 + -3m + (5 * m + m * m)) = 0
(-15 + -3m + (5m + m2)) = 0

Combine like terms: -3m + 5m = 2m
(-15 + 2m + m2) = 0

Solving
-15 + 2m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-5 + -1m)(3 + -1m) = 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 '(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 = {-5, 3}