Answer:
c. (x+3)(4x2)+(x+3)(6) (see the original solution on the bottom)
Step-by-step explanation:
Solve for x over the real numbers:
(x + 3) (4 x^2 + 5) = 0
Split into two equations:
x + 3 = 0 or 4 x^2 + 5 = 0
Subtract 3 from both sides:
x = -3 or 4 x^2 + 5 = 0
Subtract 5 from both sides:
x = -3 or 4 x^2 = -5
Divide both sides by 4:
x = -3 or x^2 = -5/4
x^2 = -5/4 has no solution since for all x on the real line, x^2 >=0 and -5/4<0:
Answer: x = -3
____________________________
Solve for x over the real numbers:
2 (x + 3) (2 x^2 + 3) = 0
Divide both sides by 2:
(x + 3) (2 x^2 + 3) = 0
Split into two equations:
x + 3 = 0 or 2 x^2 + 3 = 0
Subtract 3 from both sides:
x = -3 or 2 x^2 + 3 = 0
Subtract 3 from both sides:
x = -3 or 2 x^2 = -3
Divide both sides by 2:
x = -3 or x^2 = -3/2
x^2 = -3/2 has no solution since for all x on the real line, x^2 >=0 and -3/2<0:
Answer: x = -3
