Question 387723
Because "Eric" is applying the "zero product" principle to a product that is clearly not equal to zero.
As they say in the old country..."You can't do that there 'ere"
Here's the correct solution:
{{{(x-1)(x-2) = 30}}} Multiply the factors on the left side.
{{{x^2-3x+2 = 30}}} Subtract 30 from both sides.
{{{x^2-3x-28 = 0}}} Solve the quadratic equation by factoring.
{{{(x+4)(x-7) = 0}}} Here you can apply the zero product principle.
{{{x+4 = 0}}} or {{{x-7 = 0}}} so...
{{{x = -4}}} or {{{x = 7}}}
The zero product principle states:
If {{{a*b = 0}}} then either {{{a = 0}}} or {{{b = 0}}} or both.
So:
{{{(x-1)(x-2) = 30}}} therefore {{{x-1 = 30}}} or {{{x-2 = 30}}} is not valid.