(M-5)(M-6)=0

Solution for (M-5)(M-6)=0 equation:

Simplifying
(M + -5)(M + -6) = 0

Reorder the terms:
(-5 + M)(M + -6) = 0

Reorder the terms:
(-5 + M)(-6 + M) = 0

Multiply (-5 + M) * (-6 + M)
(-5(-6 + M) + M(-6 + M)) = 0
((-6 * -5 + M * -5) + M(-6 + M)) = 0
((30 + -5M) + M(-6 + M)) = 0
(30 + -5M + (-6 * M + M * M)) = 0
(30 + -5M + (-6M + M2)) = 0

Combine like terms: -5M + -6M = -11M
(30 + -11M + M2) = 0

Solving
30 + -11M + M2 = 0

Solving for variable 'M'.

Factor a trinomial.
(5 + -1M)(6 + -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 '(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 = {5, 6}