Solve for `x.`  `x^3+5x^2+6x = 0.`

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degeneratecircle | High School Teacher | (Level 2) Associate Educator

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First, we factor out the `x` to get


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


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