Solve for x over the real numbers:
(2 x + 3)^2 - 4 (2 x + 3) - 12 = 0
Expand out terms of the left hand side:
4 x^2 + 4 x - 15 = 0
The left hand side factors into a product with two terms:
(2 x - 3) (2 x + 5) = 0
Split into two equations:
2 x - 3 = 0 or 2 x + 5 = 0
Add 3 to both sides:
2 x = 3 or 2 x + 5 = 0
Divide both sides by 2:
x = 3/2 or 2 x + 5 = 0
Subtract 5 from both sides:
x = 3/2 or 2 x = -5
Divide both sides by 2:
Answer: x = 3/2 or x = -5/2