(a+3)(a+6)=

Solution for (a+3)(a+6)= 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 = 9a
(18 + 9a + a2) = 0

Solving
18 + 9a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6 + a)(3 + a) = 0

Subproblem 1
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 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 + a = 0 + -6

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

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

Simplifying
a = -6
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

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