solve for:(x^2)(e^-2x)-(x)(e^-2x)=0
You have a common factor of e^(-2x), so your equation simplifies to,
e^(-2x){x^2 - x} = 0
which devolves to,
x^2 - x = 0
or,
x(x - 1) = 0
giving the solutions,
x = 0, x = 1, both of which are valid for the common term e^(-2x)
Answer: x = 0, x = 1