1. The problem is to solve the quadratic equation $$32x + 24x = 0$$. 2. Combine like terms: $$32x + 24x = (32 + 24)x = 56x$$. 3. So the equation simplifies to $$56x = 0$$. 4. To solve for $x$, divide both sides by 56: $$x = \frac{0}{56} = 0$$. 5. Therefore, the solution to the equation is $$x = 0$$. This means the only value of $x$ that satisfies the equation is zero.