(3a+2)(a+3)=0

Solution for (3a+2)(a+3)=0 equation:

Simplifying
(3a + 2)(a + 3) = 0

Reorder the terms:
(2 + 3a)(a + 3) = 0

Reorder the terms:
(2 + 3a)(3 + a) = 0

Multiply (2 + 3a) * (3 + a)
(2(3 + a) + 3a * (3 + a)) = 0
((3 * 2 + a * 2) + 3a * (3 + a)) = 0
((6 + 2a) + 3a * (3 + a)) = 0
(6 + 2a + (3 * 3a + a * 3a)) = 0
(6 + 2a + (9a + 3a2)) = 0

Combine like terms: 2a + 9a = 11a
(6 + 11a + 3a2) = 0

Solving
6 + 11a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + a)(2 + 3a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(2 + 3a)' equal to zero and attempt to solve:

Simplifying
2 + 3a = 0

Solving
2 + 3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3a = 0 + -2
3a = 0 + -2

Combine like terms: 0 + -2 = -2
3a = -2

Divide each side by '3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
Solution
a = {-3, -0.6666666667}