Question about quadratic equation

Question

Suppose a quadratic equation whose roots are 3 and -2, so the equation is (x-3)(x+2) = 0
So, from here we get, x-3 = 0 and, x+2 = 0 Since, both equations equal to zero, we can equate these two, x-3 = x+2 So, -3 = 2 ? Where did I go wrong?

Answer 1

You are wrong when you say that

x-3=0 AND x+2=0

You correctly reduced the given quadratic to

(x-3)(x+2)=0

Hence this equation will be satisfied if and only if any ONE of the conditions are satisfied....ie....Either

x-3=0

OR

x+2=0

(Since 0x(any no.)=0)

Hence you get two solutions

x=3

AND

x=-2

Obviously x can take only a single value at a time.