(m-12)(m+5)=0

Solution for (m-12)(m+5)=0 equation:

Simplifying
(m + -12)(m + 5) = 0

Reorder the terms:
(-12 + m)(m + 5) = 0

Reorder the terms:
(-12 + m)(5 + m) = 0

Multiply (-12 + m) * (5 + m)
(-12(5 + m) + m(5 + m)) = 0
((5 * -12 + m * -12) + m(5 + m)) = 0
((-60 + -12m) + m(5 + m)) = 0
(-60 + -12m + (5 * m + m * m)) = 0
(-60 + -12m + (5m + m2)) = 0

Combine like terms: -12m + 5m = -7m
(-60 + -7m + m2) = 0

Solving
-60 + -7m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-5 + -1m)(12 + -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 '(12 + -1m)' equal to zero and attempt to solve:

Simplifying
12 + -1m = 0

Solving
12 + -1m = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1m = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1m = 0 + -12
-1m = 0 + -12

Combine like terms: 0 + -12 = -12
-1m = -12

Divide each side by '-1'.
m = 12

Simplifying
m = 12
Solution
m = {-5, 12}