(a-5)(a-6)=0

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

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

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

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

Multiply (-5 + a) * (-6 + a)
(-5(-6 + a) + a(-6 + a)) = 0
((-6 * -5 + a * -5) + a(-6 + a)) = 0
((30 + -5a) + a(-6 + a)) = 0
(30 + -5a + (-6 * a + a * a)) = 0
(30 + -5a + (-6a + a2)) = 0

Combine like terms: -5a + -6a = -11a
(30 + -11a + a2) = 0

Solving
30 + -11a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5 + -1a)(6 + -1a) = 0

Subproblem 1
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {5, 6}