(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.
(-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}