What most naturally follows?

How to solve quadratic equations with the " transforming method " 
Recall the rule of signs. 
If a and c have different signs, roots have different signs if a and c have same sign, roots have same sign. If a and b have different signs, both roots are positive.
If a and b have same sign, both roots are negative. Transform the equation in standard form ax^2 + bx + c = 0 (1) into a new equation, with a = 1, and the constant c = a * c.