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

Solution for (m-5)(m+1)=0 equation:

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

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

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

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

Combine like terms: -5m + 1m = -4m
(-5 + -4m + m2) = 0

Solving
-5 + -4m + m2 = 0

Solving for variable 'm'.

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

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

Simplifying
-1 + -1m = 0

Solving
-1 + -1m = 0

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

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

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

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

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

Simplifying
m = -1
Subproblem 2
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
Solution
m = {-1, 5}