Solve a product of binomials raised to a power for x

Question

Im trying to solve this equation for x in terms of a, b, c, d, and k:
$k=((a+bx)^b)*((c+dx)^d)$
B and D are positive integers, and A and C are positive or zero and not necessarily integers. This is for a function in a computer program I am coding. I'm unsure where to even begin with this problem and have asked several friends who teach math and science and they were unable to make any progress as well. Any help would be greatly appreciated.

Answer 1

Why not try coding a root finder algorithm to solve your equation numerically? E.g. consider applying the Bisection algorithm or Newton's Method to the function $$f(x) = (a+bx)^b \cdot (c+dx)^d-k.$$

Note that the root(s) of $f$ are precisely the solution(s) of your equation.

Also note that on most computer systems, such algorithms come in prepackaged libraries. If you describe your computing environment, I can try to help you track down the needed libraries. Alternatively, both methods are very easy to implement yourself directly.