Answer
$x=-\frac{3}{2}$ or $x=\frac{1}{2}$.
Work Step by Step
By factorization, we have
$$4x^2 +4 x-3=(2x+3)(2x-1)=0.$$
Then we have
$$(2x+3) =0, \quad \text{or} \quad (2x-1)=0$$
that is $x=-\frac{3}{2}$ or $x=\frac{1}{2}$.
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