What is the standard form of the equation

What is the standard form of the equation of the conic:
4x^2 - 5y^2 - 16x - 30y - 9 = 0
Can you please show the steps? Thanks!

4x^2 - 5y^2 - 16x - 30y - 9 = 0
4x^2 - 16x - 5y^2 - 30y = 9
4 * (x^2 - 4x) - 5 * (y^2 + 6y) = 9
4 * (x^2 - 4x + 4) - 5 * (y^2 + 6y + 9) = 9 + 4 * 4 - 5 * 9
4 * (x - 2)^2 - 5 * (y + 3)^2 = 9 + 16 - 45
4 * (x - 2)^2 - 5 * (y + 3)^2 = -20
5 * (y + 3)^2 - 4 * (x - 2)^2 = 20
5 * (y + 3)^2 = 20 + 4 * (x - 2)^2
(y + 3)^2 = (1/5) * (20 + 4 * (x - 2)^2)
(y + 3) = +/- sqrt(1/5) * sqrt(20 + 4 * (x - 2)^2)
y = -3 +/- (1/5) * sqrt(5) * sqrt(4) * sqrt(5 + (x - 2)^2)
y = -3 +/- (1/5) * sqrt(5) * 2 * sqrt(5 + x^2 - 4x + 4)
y = -3 +/- (2 * sqrt(5) / 5) * sqrt(x^2 - 4x + 9)

4x^2 - 5y^2-16x-30y-9=0
-5y^2 +4x^2-30y-16x-9=0

there's only one step its easy