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(x + 3) = 0. Set each factor equal to zero: x = 0 or x = -3.

In general, ax^2 + bx = 0 factors to x(ax + b) = 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.