Solve for `x.`  `x^3+5x^2+6x = 0.`

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First, we factor out the `x` to get

`x(x^2+5x+6)=0.`

If we can find two numbers that multiply to `6` and add to `5` , we can factor further. Since `3*2=6` and `3+2=5,` this means that

`x(x^2+5x+6)=x(x+3)(x+2).`

By the Zero Product Property (see the link for details), this equals zero when `x=0, x=-3,` and `x=-2.` Thus, the three solutions are

`0,-3,-2.`

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