Answer:
x = -3
Step-by-step explanation:
Solve for x over the real numbers:
(x + 3) (3 x^2 + 2 x + 1) = 0
Split into two equations:
x + 3 = 0 or 3 x^2 + 2 x + 1 = 0
Subtract 3 from both sides:
x = -3 or 3 x^2 + 2 x + 1 = 0
Divide both sides by 3:
x = -3 or x^2 + (2 x)/3 + 1/3 = 0
Subtract 1/3 from both sides:
x = -3 or x^2 + (2 x)/3 = -1/3
Add 1/9 to both sides:
x = -3 or x^2 + (2 x)/3 + 1/9 = -2/9
Write the left hand side as a square:
x = -3 or (x + 1/3)^2 = -2/9
(x + 1/3)^2 = -2/9 has no solution since for all x on the real line, (x + 1/3)^2 >=0 and -2/9<0:
Answer: x = -3
