Recall that if a product of two factors is equal to zero, then at least one of the factors must be equal to zero:
If $ab=0$, then either $a=0$ or $b=0$.
We can use this important rule to solve quadratic equations:
Rewrite your quadratic equation in standard form: $ax^{2}+bx+c=0$.
If possible, factor the quadratic expression on the left side of the equation. If the expression is not factorable, try a different technique.
Set each factor equal to zero and solve the resulting linear equation for $x$.
Quadratic equations: factoring.
The Quadratic Formula
You should have the quadratic formula memorized. If $ax^{2}+bx+c=0$, where $a \neq 0$, then all real-valued solutions are given by
$$
x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}.
$$
The expression $b^{2}-4ac$ is called the discriminant. Recall:
$b^{2}-4ac > 0$ implies the quadratic equation has two solutions.
$b^{2}-4ac = 0$ implies the quadratic equation has one solution.
$b^{2}-4ac < 0$ implies the quadratic equation has no solutions. In this case the quadratic expression $ax^{2}+bx+c$ does not factor over the real numbers and is called an irreducible quadratic.