Zero product property

[LivedKrad]

128x = 6x^2: Solve with the zero product property.

I am totally confused..

[Maddox]

128(0) = 6(0^2) so one answer is x = 0

dividing both sides by x gives you
128 = 6x so another is x = 64/3

[Yoni]

I think what they mean is:

128x = 6x^2
6x^2 - 128x = 0
x(6x - 128) = 0

==> The product of "x" and "6x - 128" is 0.
The so-called "zero product property" probably means: If the product of two numbers is zero, one of them must be zero.
So: x is zero, or 6x - 128 is zero.
x = 0 or 6x = 128
x = 0 or x = 128/6