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

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

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

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

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

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

Combine like terms: 8a + -3a = 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}