Solve for y over the real numbers:
(y + 2)^2 = 2 y^2 + 12 y + 19
Subtract 2 y^2 + 12 y + 19 from both sides:
-19 - 12 y - 2 y^2 + (y + 2)^2 = 0
Expand out terms of the left hand side:
-y^2 - 8 y - 15 = 0
The left hand side factors into a product with three terms:
-(y + 3) (y + 5) = 0
Multiply both sides by -1:
(y + 3) (y + 5) = 0
Split into two equations:
y + 3 = 0 or y + 5 = 0
Subtract 3 from both sides:
y = -3 or y + 5 = 0
Subtract 5 from both sides:
Answer: y = -3 or y = -5