1. **Problem statement:** Solve the equation $$3x - 10 = 2 \cdot 2^2 - 9$$. 2. **Recall the order of operations:** Calculate exponents first, then multiplication/division, and finally addition/subtraction. 3. **Calculate the right side:** $$2^2 = 4$$ $$2 \cdot 4 = 8$$ $$8 - 9 = -1$$ 4. **Rewrite the equation:** $$3x - 10 = -1$$ 5. **Isolate the variable term:** Add 10 to both sides: $$3x = -1 + 10$$ $$3x = 9$$ 6. **Solve for $x$:** Divide both sides by 3: $$x = \frac{9}{3} = 3$$ 7. **Final answer:** $$x = 3$$