Common Factor First

An equation like ${x}^{3} = 25x$ tempts you to divide both sides by x. That gives ${x}^{2} = 25$, so x is 5 or -5. But 0 works too: 0 cubed is 0, and 25 times 0 is 0. Dividing by x threw that answer away, because dividing by x is only allowed when x is not 0.

The safe route is to get 0 on one side and factor. In ${x}^{3}-25x = 0$ both terms hold x, so take it out: $x\left({x}^{2}-25\right) = 0$. A product is 0 only when one of its factors is 0, so split into cases: $x = 0$, or ${x}^{2}-25 = 0$, which gives 5 and -5. That makes three answers, and a cubic can have up to three.