What is wrong with:
52 - x² + x = 10 ?
First of all it doesn't have 0 on the right side.
So we add -10 to both sides:
42 - x² + x = 0
Secondly it is not in descending order,
so we write the x² term first, then the
x-term and finally the constant
-x² + x + 42 = 0
Thirdly the leading coefficient (the coefficient of the
x² term) should be positive, so we multiply it
through by -1, changing all the signs
x² - x - 42 = 0
Now it's easy to factor as
(x - 7)(x + 6) = 0
and solve with the zero-factor property:
x - 7 = 0; x + 6 = 0
x = 7; x = -6
Edwin