$2 {\cos }^2\left(x\right)\+3 {\cos }^2\left(x\right)-5 {\sin }^2\left(x\right)\+7 \sin \left(x\right)\=0$

$5{\cos \left(x\right)}^2-5{\sin \left(x\right)}^2\+7\sin \left(x\right)\=0$

$\mathrm{Student}\left[\mathrm{Precalculus}\right]\left[\mathrm{CompleteSquare}\right]\left(\,\left[\cos \left(x\right)\,\sin \left(x\right)\right]\right)$

$-5{\left(\sin \left(x\right)-\frac{7}{10}\right)}^2\+5{\cos \left(x\right)}^2\+\frac{49}{20}\=0$