Answer
Zero-Factor Property
Work Step by Step
In the form $ax^2+bx+c=0,$ the given equation, $
3x^2=2-5x
,$ is equivalent to
\begin{align*}
3x^2+5x-2&=0
.\end{align*}
Using $ax^2+bx+c=0,$ the equation above has
\begin{align*}
a=
3
,\text{ }b=
5
,\text{ and }c=
-2
.\end{align*}
Using the discriminant of a quadratic equation, which is given by $b^2-4ac,$ then
\begin{align*}
b^2-4ac&=
(5)^2-4(3)(-2)
\\&=
25+24
\\&=
49
\\&=
7^2
.\end{align*}
Since the discriminant is a perfect square, and all the coefficients of the given equation are integers, then the given equation can be factored. The factors can then be equated to zero. Hence, the Zero-Factor Property is the most appropriate way to solve the given equation.
