(a-3)(a-5)=0

Solution for (a-3)(a-5)=0 equation:

Simplifying
(a + -3)(a + -5) = 0

Reorder the terms:
(-3 + a)(a + -5) = 0

Reorder the terms:
(-3 + a)(-5 + a) = 0

Multiply (-3 + a) * (-5 + a)
(-3(-5 + a) + a(-5 + a)) = 0
((-5 * -3 + a * -3) + a(-5 + a)) = 0
((15 + -3a) + a(-5 + a)) = 0
(15 + -3a + (-5 * a + a * a)) = 0
(15 + -3a + (-5a + a2)) = 0

Combine like terms: -3a + -5a = -8a
(15 + -8a + a2) = 0

Solving
15 + -8a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + -1a)(5 + -1a) = 0

Subproblem 1
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
Subproblem 2
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
Solution
a = {3, 5}