1. **State the problem:** Solve the quadratic equation $$10x^2 - 12x = 0$$ by any method. 2. **Formula and rules:** To solve quadratic equations, one common method is factoring. If the equation can be factored as $$a(x)(b(x)) = 0$$, then by the zero product property, either $$a(x) = 0$$ or $$b(x) = 0$$. 3. **Factor the equation:** $$10x^2 - 12x = 0$$ Factor out the greatest common factor (GCF), which is $$2x$$: $$2x(5x - 6) = 0$$ 4. **Apply zero product property:** Set each factor equal to zero: $$2x = 0$$ or $$5x - 6 = 0$$ 5. **Solve each equation:** For $$2x = 0$$: $$x = \cancel{\frac{0}{2}}0$$ For $$5x - 6 = 0$$: Add 6 to both sides: $$5x = 6$$ Divide both sides by 5: $$x = \cancel{\frac{6}{5}}\frac{6}{5}$$ 6. **Final answer:** $$x = 0$$ or $$x = \frac{6}{5}$$ This means the solutions to the quadratic equation are $$0$$ and $$\frac{6}{5}$$.