(a+3)(a-9)=0

Solution for (a+3)(a-9)=0 equation:

Simplifying
(a + 3)(a + -9) = 0

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

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

Multiply (3 + a) * (-9 + a)
(3(-9 + a) + a(-9 + a)) = 0
((-9 * 3 + a * 3) + a(-9 + a)) = 0
((-27 + 3a) + a(-9 + a)) = 0
(-27 + 3a + (-9 * a + a * a)) = 0
(-27 + 3a + (-9a + a2)) = 0

Combine like terms: 3a + -9a = -6a
(-27 + -6a + a2) = 0

Solving
-27 + -6a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a)(9 + -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 '(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
Solution
a = {-3, 9}