Answer
$x = 2$ or $x = 1$
Work Step by Step
Simplify by dividing all terms by their greatest common factor, $3$:
$x^2 - 3x + 2 = 0$
We now have a quadratic expression in the form $x^2 + bx + c$.
Find factors of $c$, which is $2$ in this case, whose sum is $b$, which is $-3$ in this case.
List of possible factors of $2$:
$-2$ and $-1$
$2$ and $1$
The first pair of factors has a sum of $-3$.
Rewrite the equation using the factors:
$(x - 2)(x - 1) = 0$
Use the Zero Product Property to set each factor equal to $0$ and solve:
First factor:
$x - 2 = 0$
$x = 2$
Second factor:
$x - 1 = 0$
$x = 1$
