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

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

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

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

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

Combine like terms: 9a + -2a = 7a
(-6 + 7a + 3a2) = 0

Solving
-6 + 7a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a)(2 + -3a) = 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 '(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}