Answer
It is incorrect to equate each factor of the equation $(x-2)(x+1)=5$ to $5$. The Zero Product Property can only be used if the factors are equal to $0.$
Work Step by Step
In the given equation, $x^2-x-2=5,$ the right side of the equation is not equal to zero. Hence, the left side cannot be factored and then the factors equated to $5$. This method can only be done if the equation is equal to zero.
The correct method is to transpose $5$ to the left side and then to combine with $-2.$ Then the resulting equation can be solved by factoring (if factorable) or by the Quadratic Formula.
