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