Answer: 0, 5/6
To solve the equation 5x^3 e^(-2x) - 6x^4 e^(-2x) = 0:
Factor out x^3 e^(-2x) from both terms to get:
x^3 e^(-2x) (5 - 6x) = 0
This equation is satisfied when either x^3 e^(-2x) = 0 or 5 - 6x = 0.
Solving x^3 e^(-2x) = 0 gives x = 0 (since e^(-2x) is always positive and nonzero).
Solving 5 - 6x = 0 gives x = 5/6.
Therefore, the solutions to the equation are x = 0 and x = 5/6, and the comma-separated list of answers is (0, 5/6).