Cubic question please help

Find a cubic function whose graph touches the x-axis at x=−4, passes through the origin
and has a value of 10 when x = 5.
The answer is y = 2/81x(x + 4)2
Please show some working

touches the x-axis at x=-4
=> two zeroes at x = -4
=> (x+4)^2 is a factor

Passes through the origin
=> one zero at x=0
=> x is a factor

And since it's a cubic, it's only got three factors, so
=> y = kx(x+4)^2
... where k is a constant which we haven't worked out yet.

But when x=5, y=10
=> 10 = k(5)(5+4)^2
=> 10 = k(5)(81)
=> k = 2/81