(a+3)(a-6)=0

Solution for (a+3)(a-6)=0 equation:

Simplifying
(a + 3)(a + -6) = 0

Reorder the terms:
(3 + a)(a + -6) = 0

Reorder the terms:
(3 + a)(-6 + a) = 0

Multiply (3 + a) * (-6 + a)
(3(-6 + a) + a(-6 + a)) = 0
((-6 * 3 + a * 3) + a(-6 + a)) = 0
((-18 + 3a) + a(-6 + a)) = 0
(-18 + 3a + (-6 * a + a * a)) = 0
(-18 + 3a + (-6a + a2)) = 0

Combine like terms: 3a + -6a = -3a
(-18 + -3a + a2) = 0

Solving
-18 + -3a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a)(6 + -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 '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-3, 6}