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

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

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

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

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

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

Combine like terms: 5a + -3a = 2a
(-15 + 2a + a2) = 0

Solving
-15 + 2a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -1a)(3 + -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 '(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 = {-5, 3}