Final answer:
The solutions to the equation x²(x + 2)(x - 5) = 0 are x = 0, x = -2, and x = 5, which are found by setting each factor equal to zero separately.
Step-by-step explanation:
To solve the equation x²(x + 2)(x - 5) = 0, we make use of the property that if the product of several factors equals zero, then at least one of the factors must be zero. Thus, we set each factor equal to zero:
From x² = 0, we find x = 0. From x + 2 = 0, we subtract 2 from both sides to get x = -2. From x - 5 = 0, we add 5 to both sides to obtain x = 5.
Therefore, the solutions to the equation are x = 0, x = -2, and x = 5. These are the points where the function crosses or touches the x-axis.