(a-2)(a-6)=0

Solution for (a-2)(a-6)=0 equation:

Simplifying
(a + -2)(a + -6) = 0

Reorder the terms:
(-2 + a)(a + -6) = 0

Reorder the terms:
(-2 + a)(-6 + a) = 0

Multiply (-2 + a) * (-6 + a)
(-2(-6 + a) + a(-6 + a)) = 0
((-6 * -2 + a * -2) + a(-6 + a)) = 0
((12 + -2a) + a(-6 + a)) = 0
(12 + -2a + (-6 * a + a * a)) = 0
(12 + -2a + (-6a + a2)) = 0

Combine like terms: -2a + -6a = -8a
(12 + -8a + a2) = 0

Solving
12 + -8a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + -1a)(6 + -1a) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
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 = {2, 6}