(a-2)(a-3)=0

Solution for (a-2)(a-3)=0 equation:

Simplifying
(a + -2)(a + -3) = 0

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

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

Multiply (-2 + a) * (-3 + a)
(-2(-3 + a) + a(-3 + a)) = 0
((-3 * -2 + a * -2) + a(-3 + a)) = 0
((6 + -2a) + a(-3 + a)) = 0
(6 + -2a + (-3 * a + a * a)) = 0
(6 + -2a + (-3a + a2)) = 0

Combine like terms: -2a + -3a = -5a
(6 + -5a + a2) = 0

Solving
6 + -5a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + -1a)(3 + -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 '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {2, 3}