(m-2)(m-3)-12=0

Solution for (m-2)(m-3)-12=0 equation:

Simplifying
(m + -2)(m + -3) + -12 = 0

Reorder the terms:
(-2 + m)(m + -3) + -12 = 0

Reorder the terms:
(-2 + m)(-3 + m) + -12 = 0

Multiply (-2 + m) * (-3 + m)
(-2(-3 + m) + m(-3 + m)) + -12 = 0
((-3 * -2 + m * -2) + m(-3 + m)) + -12 = 0
((6 + -2m) + m(-3 + m)) + -12 = 0
(6 + -2m + (-3 * m + m * m)) + -12 = 0
(6 + -2m + (-3m + m2)) + -12 = 0

Combine like terms: -2m + -3m = -5m
(6 + -5m + m2) + -12 = 0

Reorder the terms:
6 + -12 + -5m + m2 = 0

Combine like terms: 6 + -12 = -6
-6 + -5m + m2 = 0

Solving
-6 + -5m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-1 + -1m)(6 + -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 '(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
Solution
m = {-1, 6}