(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.
(-6 + -1a)(3 + -1a) = 0

Subproblem 1
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
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 = {-6, 3}