Answer:
[tex]\large\boxed{q=-9\ or\ q=2}[/tex]
Step-by-step explanation:
[tex]4q^2+3q=3q^2-4q+18\qquad\text{subtract}\ 3q^2\ \text{from both sides}\\\\q^2+3q=-4q+18\qquad\text{add}\ 4q\ \text{to both sides}\\\\q^2+7q=18\qquad\text{subtract 18 from both sides}\\\\q^2+7q-18=0\\\\q^2+9q-2q-18=0\\\\q(q+9)-2(q+9)+0\\\\(q+9)(q-2)=0\iff q+9=0\ \vee\ q-2=0\\\\q+9=0\qquad\text{subtract 9 from both sides}\\\boxed{q=-9}\\\\q-2=0\qquad\text{add 2 to both sides}\\\boxed{q=2}[/tex]
