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
