(a-5)(a+3)=

Solution for (a-5)(a+3)= 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.
(-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}