Answer
$-\frac{15}{2}$
Work Step by Step
$4(x+6)+3=-3$
$4x+24+3=-3$
$4x+27=-3$
$4x=-3-27$
$4x=-30$
$x=-\frac{30}{4}=-\frac{15}{2}$
Check:
$4(-\frac{15}{2}+6)+3=-3$
$4(\frac{-15+2(6)}{2})+3=-3$
$4(\frac{-15+12}{2})+3=-3$
$4(\frac{-3}{2})+3=-3$
$2(-3)+3=-3$
$-6+3=-3$
$-3=-3$
$0=0$
Therefore, the solution checks out.