(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 = -2a
(-15 + -2a + a2) = 0

Solving
-15 + -2a + 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}