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You get vertical asymptotes because the x-value causes you to try to divide by 0.
If you look at the denominator, the x-values of 0, 1, and -5 all will make the denominator equal to 0, making the whole function explode.
You find these by solving 3x(x-1)(x+5)=0.
That's your answer: 0, 1, and -5