(a-3)(a+8)=0

Solution for (a-3)(a+8)=0 equation:

Simplifying
(a + -3)(a + 8) = 0

Reorder the terms:
(-3 + a)(a + 8) = 0

Reorder the terms:
(-3 + a)(8 + a) = 0

Multiply (-3 + a) * (8 + a)
(-3(8 + a) + a(8 + a)) = 0
((8 * -3 + a * -3) + a(8 + a)) = 0
((-24 + -3a) + a(8 + a)) = 0
(-24 + -3a + (8 * a + a * a)) = 0
(-24 + -3a + (8a + a2)) = 0

Combine like terms: -3a + 8a = 5a
(-24 + 5a + a2) = 0

Solving
-24 + 5a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-8 + -1a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-8 + -1a)' equal to zero and attempt to solve:

Simplifying
-8 + -1a = 0

Solving
-8 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1a = 0 + 8
-1a = 0 + 8

Combine like terms: 0 + 8 = 8
-1a = 8

Divide each side by '-1'.
a = -8

Simplifying
a = -8
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 = {-8, 3}