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
