Want to 'Solve' a piecewise equation for a common term

*To*: mathgroup at smc.vnet.net*Subject*: [mg79756] Want to 'Solve' a piecewise equation for a common term*From*: "misnomer at gmail.com" <misnomer at gmail.com>*Date*: Fri, 3 Aug 2007 06:34:57 -0400 (EDT)

I've been battling to try to get a solution to my equation, but it requires solving of a piecewise function, which I cannot work out how to do. Say I have a piecewise function of the form temp = Piecewise[{ { 2*N*x, x < 0}, { N*x, x >= 0} }] I want to either solve this via Solve[1==temp, N] and either get, with the inequalities, N -> Piecewise[{ {1/(2*x), x < 0}, {1/x, x >= 0} }] or just get mathematica to realise that there is a common term - N, and factor it out to, say, N * Piecewise[{ {2*x, x < 0}, {x, x >= 0} }] from where solve can handle it perfectly well. Is this type of operation possible, or am I stuck editing them by hand?