Answer
The solutions are $x=1$ and $x=-\dfrac{3}{4}$
Work Step by Step
$-4x^{2}+x=-3$
Take all terms to the right side of the equation:
$0=4x^{2}-x-3$
Rearrange:
$4x^{2}-x-3=0$
Factor the left side of the equation:
$(4x+3)(x-1)=0$
Using the zero-factor property, set both factors equal to $0$ and solve each individual equation for $x$:
$4x+3=0$
$4x=-3$
$x=-\dfrac{3}{4}$
$x-1=0$
$x=1$
The solutions are $x=1$ and $x=-\dfrac{3}{4}$
