Solve x^2+5x+6=0 by factorising

First of all, when we expand brackets we know that the x will be at the start of the brackets 

(x    )(x    )= 0

Look a the equation again, x²+5x+6=0. All of our numbers are positive so we know that we don't need any subtraction or negative signs in our equation 

(x+  )(x+  )= 0

Then to fill in the gaps we need to find pairs of numbers that multiply to 6 

1x6=6

2x3=6

We then need to look at those pairs of numbers and see which pairs add to 5. 

1+6=7 NO

2+3=5 YES

So we can now take this pair of numbers and put it into the equation to double check

(x+2 )(x+3 )= 0

Lets expand the brackets to double check.

x*x=x²

x*3= 3x

2*x=2x

2*3=6

lets put those together to make the original equation 

x²+5x+6=0 so yes, we know our factorising of the equation is correct. 

Now we can solve the equations 

(x+2 )(x+3 )= 0

If they equal zero when multipled then one or other of the equations must equal zero on its own. So we can solve for x by making both equations equal to zero. 

(x+2)=0          (x+3)=0

x+2 = 0           x+3=0

we can now solve the equation by performing the opposite function on the numbers to get x on its own 

the 2 is added on the left, so to move it to the right we have to subtract it, same for the 3

x=0-2             x=0-3

x= -2              x= -3

So! x= -2 OR x= -3