2(a-6)(a-4)=0

Solution for 2(a-6)(a-4)=0 equation:

Simplifying
2(a + -6)(a + -4) = 0

Reorder the terms:
2(-6 + a)(a + -4) = 0

Reorder the terms:
2(-6 + a)(-4 + a) = 0

Multiply (-6 + a) * (-4 + a)
2(-6(-4 + a) + a(-4 + a)) = 0
2((-4 * -6 + a * -6) + a(-4 + a)) = 0
2((24 + -6a) + a(-4 + a)) = 0
2(24 + -6a + (-4 * a + a * a)) = 0
2(24 + -6a + (-4a + a2)) = 0

Combine like terms: -6a + -4a = -10a
2(24 + -10a + a2) = 0
(24 * 2 + -10a * 2 + a2 * 2) = 0
(48 + -20a + 2a2) = 0

Solving
48 + -20a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -10a + a2) = 0

Factor a trinomial.
2((4 + -1a)(6 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
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 = {4, 6}