Your product of 12 and 18 is not 125 (it is 216), but otherwise, yes, this is a linear equation, and you want to calculate an integrating factor.
How would I go about solving this form of differential equation?
(dx/dt) = (12b)(18bt-x)
So it becomes
(dx/dt) = (125(b^2)t)-(12bx)
Use the integrating factor method?
(dx/dt) + (12bx) = (125(b^2)t)
Or not - I am totally stumped with this...