Answer:
-6
0
Step-by-step explanation:
By observation we can see one solution is x=0 since this will give us
(0-3)(0+9)=(-3)(9)=-27 which is the result on the right hand side.
Now this is a quadratic equation so it should have another solution. This one doesn't seem as obvious to me.
The goal normally is to get 0 on side and factor if possible or use quadratic formula. There is also completing the square.
So I'm going to multiply (x-3)(x+9) using foil.
First: x(x)=x^2
Outer: x(9)=9x
Inner: -3(x)=-3x
Last: -3(9)=-27
---------------------Combine like terms:
x^2+6x-27
So the equation is:
x^2+6x-27=-27
Add 27 on both sides:
x^2+6x+0=0
x^2+6x=0
Factor x out:
x(x+6)=0
In order for these equation to be true one of the left hand factors need to be 0.
Let's find when x is 0, well that is when x=0.
Let's find when x+6 is 0.
x+6=0 can be solved by subtracting 6 on both sides:
x=-6
The solutions are -6 and 0.
We already checked x=0.
Let's check x=-6:
Plugging in -6 where x is in the given equation:
(-6-3)(-6+9)
(-9)(3)
-27 which is the same as right hand side.
