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

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

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

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

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

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

Combine like terms: 5a + -1a = 4a
(-5 + 4a + a2) = 0

Solving
-5 + 4a + a2 = 0

Solving for variable 'a'.

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

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