solve x^2e^x+9x^ex=0

Answer 1

x^2e^x + 9xe^x = 0.
Factor out e^x:
e^x(x^2+9x) = 0,
Divide both sids by e^x:
x^2 + 9x = 0,
x(x+9) = 0,
x = 0.

x + 9 = 0,
x = -9.

Solution Set: x = 0, and x =-9.