Answer
$q=2$ or $q=-9$
Work Step by Step
$4q^2+3q=3q^2-4q+18$
$q^2+7q-18=0$
$q^2-2q+9q-18=0$
$(q-2)(q+9)=0$
$q-2=0$ or $q+9=0$
$q=2$ or $q=-9$
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