Solve x²+5x+6=0

To solve the quadratic equation $x^2+5x+6=0$, we can factor the quadratic expression.

We are looking for two numbers that multiply to 6 and add up to 5. These numbers are 2 and 3.

So, we can factor the equation as:
$(x+2)(x+3)=0$

For the product of two factors to be zero, at least one of the factors must be zero.
Therefore, we set each factor equal to zero and solve for x:

$x+2=0$
$x=-2$

or

$x+3=0$
$x=-3$

The solutions for the equation $x^2+5x+6=0$ are $x=-2$ and $x=-3$.