Answer
$x = 4$ and $x = 3$
Work Step by Step
Rewrite the equation so all terms are on the left side of the equation:
$x^2 - 7x + 12 = 0$
We now have a quadratic expression in the form $ax^2 + bx + c$.
Find factors whose product is $ac$, which is $1 \cdot 12$ or $12$ in this case, but sum up to $b$, which is $-7$ in this case.
List possible factors:
$-4$ and $-3$
$-6$ and $-2$
$-12$ and $-1$
The first option will work.
Rewrite the equation using the factors:
$(x - 4)(x - 3) = 0$
Use the Zero Product Property to set each factor equal to $0$ and solve:
First factor:
$x - 4 = 0$
$x = 4$
Second factor:
$x - 3 = 0$
$x = 3$
Therefore, the solutions are $3$ and $4$.
