#### Answer

The solutions are $x= \frac{1}{4}$ and $x= -\frac{7}{4}$.

#### Work Step by Step

The given equation is
$\Rightarrow (4x+3)^2=16$
Take square on each side.
$\Rightarrow 4x+3=\pm\sqrt{16}$
Simplify.
$\Rightarrow 4x+3=\pm4$
Solve for $x$.
$\Rightarrow x= \frac{-3\pm4}{4}$
Hence, the solutions are $x= \frac{-3+4}{4}= \frac{1}{4}$ and $x= \frac{-3-4}{4}= -\frac{7}{4}$.