Answer
$x=\frac{1}{2}$ or $x=-4$
Work Step by Step
Equation:$2x^2+7x-4=0$
Factor the trinomial.
The coefficient of $x^2$ is $2$, hence the coefficients of x in the multipliers are probably $2$ and $1$.
The coefficient of $x^0$ (the constant) is $-4$, hence the possible coefficients of the $x^0$ are:
$-2$ and $2$; or
$-1$ and $4$; or
$1$ and $-4$.
Out of these combinations, the factors that give a middle term of $7x$ are $(2x-1)(x+4)=0$.
Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
2x-1&=0 &\text{or}& &x+4=0\\
2x&=1 &\text{or}& &x=-4\\
x&=\frac{1}{2} &\text{or}& &x=-4
\end{align*}
