what is the answer to (x-2)(x+3)=0
Actually, this is a quadratic equation because when you multiply it out you get
(x - 2)(x + 3) = x^2 - 2x + 3x - 6 = x^2 + x - 6
And x^2 + x - 6 has got x to the 2nd power, so that makes it a quadratic.
When we solve x^2 + x - 6 = 0, then we are finding those values of x that will make the quadratic expression x^2 + x - 6 equal to zero.
This is easier to see if we can factorise it. This, in fact, is how we started. We started with
(x - 2)(x + 3) = 0
If we put x = 2 into the left hand bracket, we get 2 - 2 = 0. So the left hand bracket times the right hand bracket is equal to zero, which equals the right hand side (= 0).
So x = 2 is a valid solution to the quadratic equation.
Similarly, if you set x = -3 in the right hand bracket, that bracket becomes zero, and by the same argument as before, x = -3 is a solution to the quadratic equation.
Answer: the solutions are. x = 2, x = -3