College Algebra (11th Edition)

$$x=1,-3$$
$$\sqrt{-2x+3}=3-\sqrt{x+3}$$ $$-2x+3=9-6\sqrt{x+3}+(\sqrt{x+3})^2$$ $$-2x+3=12-6\sqrt{x+3}+x$$ $$-3x-9=-6\sqrt{x+3}$$ $$x+3=2\sqrt{x+3}$$ Square both sides. $$x^2+6x+9=4(x+3)$$ $$x^2+6x+9=4x+12$$ $$x^2+2x-3=0$$ $$(x+3)(x-1)=0$$ $$x=1,-3$$