(a-8)(a+9)=0

Solution for (a-8)(a+9)=0 equation:

Simplifying
(a + -8)(a + 9) = 0

Reorder the terms:
(-8 + a)(a + 9) = 0

Reorder the terms:
(-8 + a)(9 + a) = 0

Multiply (-8 + a) * (9 + a)
(-8(9 + a) + a(9 + a)) = 0
((9 * -8 + a * -8) + a(9 + a)) = 0
((-72 + -8a) + a(9 + a)) = 0
(-72 + -8a + (9 * a + a * a)) = 0
(-72 + -8a + (9a + a2)) = 0

Combine like terms: -8a + 9a = 1a
(-72 + 1a + a2) = 0

Solving
-72 + 1a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-9 + -1a)(8 + -1a) = 0

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
Subproblem 2
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
Solution
a = {-9, 8}