1. **State the problem:** Solve the equation $$4(\tan x - 1) = 3(5 - 2 \tan x)$$ for $$0 < x < 360$$ degrees. 2. **Write the equation:** $$4\tan x - 4 = 15 - 6\tan x$$ 3. **Group like terms:** Move all terms involving $$\tan x$$ to one side and constants to the other: $$4\tan x + 6\tan x = 15 + 4$$ 4. **Simplify:** $$10\tan x = 19$$ 5. **Solve for $$\tan x$$:** $$\tan x = \frac{19}{10} = 1.9$$ 6. **Find general solutions:** The tangent function has period 180 degrees, so solutions are: $$x = \arctan(1.9) + k \times 180^\circ$$ for integers $$k$$. 7. **Calculate principal value:** $$x_1 = \arctan(1.9) \approx 62.74^\circ$$ 8. **Find second solution in $$0 < x < 360$$:** $$x_2 = 62.74^\circ + 180^\circ = 242.74^\circ$$ 9. **Final answer:** $$x \approx 62.74^\circ, 242.74^\circ$$ These are the two solutions for $$x$$ in the interval $$0 < x < 360$$ degrees.