Solving by Factorization

Factorization solves $ax^2+bx+c=0$ by rewriting the left side as a product of two linear factors, then using the fact that a product of real numbers is zero only when at least one factor is zero (the zero-product rule): if $(x-\alpha)(x-\beta) = 0$ then $x = \alpha$ or $x = \beta$.

Method (the "split the middle term" technique):

1. Write the equation in the form $ax^2+bx+c=0$.
2. Find two numbers $p$ and $q$ such that $p \times q = ac$ (the product of the coefficient of $x^2$ and the constant term) and $p + q = b$ (the coefficient of $x$).
3. Split the middle term $bx$ as $px + qx$, so the equation becomes $ax^2 + px + qx + c = 0$.
4. Group the four terms in pairs and factor out the common factor from each pair.
5. The equation is now a product of two binomials equal to zero; set each binomial to zero and solve for $x$.