**Answer:**

**a = -2/3**

**Step-by-step explanation:**

Solve for a over the real numbers:

(3 a + 2) (4 a^2 - 2 a + 9) = 0

Split into two equations:

3 a + 2 = 0 or 4 a^2 - 2 a + 9 = 0

Subtract 2 from both sides:

3 a = -2 or 4 a^2 - 2 a + 9 = 0

Divide both sides by 3:

a = -2/3 or 4 a^2 - 2 a + 9 = 0

Divide both sides by 4:

a = -2/3 or a^2 - a/2 + 9/4 = 0

Subtract 9/4 from both sides:

a = -2/3 or a^2 - a/2 = -9/4

Add 1/16 to both sides:

a = -2/3 or a^2 - a/2 + 1/16 = -35/16

Write the left hand side as a square:

a = -2/3 or (a - 1/4)^2 = -35/16

(a - 1/4)^2 = -35/16 has no solution since for all a on the real line, (a - 1/4)^2 >=0 and -35/16<0:

Answer: a = -2/3