Factor, Then Split

To solve $x^{2}+5x+6 = 0$, factor the left side first. The numbers 2 and 3 add to 5 and multiply to 6, so the equation becomes $\left(x+2\right)\left(x+3\right) = 0$. Now set each factor equal to zero: $x = -2$ or $x = -3$.

To solve by factoring, write the equation with zero on one side. Factor the other side. Then set each factor equal to zero, solve each small equation, and include every different solution.

To check, substitute each answer into the original equation. At $x = -2$, you get $4-10+6 = 0$. At $x = -3$, you get $9-15+6 = 0$. Both are true, so both answers are solutions. Factoring did not only rewrite the equation. It solved it.