The GCF Route

Not every quadratic equation has a constant term. $x^{2}+3x = 0$ has no constant, so there is no pair of numbers to find. Instead, factor out the greatest common factor, $x$, as in chapter two: $x\left(x+3\right) = 0$. Set each factor equal to zero: $x = 0$ or $x = -3$.

In general, $ax^{2}+bx = 0$ factors to $x\left(ax+b\right) = 0$. The factor $x$ gives the solution $x = 0$. Keep that case, and solve the other factor for the second solution.

Do not divide both sides by $x$. It looks as if $x^{2}+3x = 0$ simplifies to $x+3 = 0$, but dividing by $x$ assumes that $x$ is not zero. That throws away the solution $x = 0$. Factor instead, and never divide by the unknown.