(a-1)(a-5)=0

Solution for (a-1)(a-5)=0 equation:

Simplifying
(a + -1)(a + -5) = 0

Reorder the terms:
(-1 + a)(a + -5) = 0

Reorder the terms:
(-1 + a)(-5 + a) = 0

Multiply (-1 + a) * (-5 + a)
(-1(-5 + a) + a(-5 + a)) = 0
((-5 * -1 + a * -1) + a(-5 + a)) = 0
((5 + -1a) + a(-5 + a)) = 0
(5 + -1a + (-5 * a + a * a)) = 0
(5 + -1a + (-5a + a2)) = 0

Combine like terms: -1a + -5a = -6a
(5 + -6a + a2) = 0

Solving
5 + -6a + a2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
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 = {1, 5}