Originally Posted by
NOX Andrew After $\displaystyle 3x^2 + 6x - 9 = 0$, you wrote $\displaystyle 3x(x - 1) = 0$, which is false. Expand the left-hand side of the false equation to see why.
Instead, divide the equation $\displaystyle 3x^2 + 6x - 9 = 0$ by $\displaystyle 3$:
$\displaystyle x^2 + 2x - 3= 0$
Then, factor the right-hand side of the equation:
$\displaystyle (x - 1)(x + 3) = 0$
Set each factor on the right-hand side of the equation equal to 0.
$\displaystyle x - 1 = 0$ or $\displaystyle x + 3 = 0$
Solve each equation in terms of x. The solutions are the critical values.