Final answer:
The solution to the inequality (x+2)(x-4)<0 is the interval -2 < x < 4, as the product is negative when one factor is negative and the other is positive.
Step-by-step explanation:
To solve the nonlinear inequality (x+2)(x-4)<0, we need to find the values of x where the product of these two factors is negative. This will occur when one factor is positive and the other is negative. We first start by identifying the zero points of each factor, which are x = -2 and x = 4.
The intervals we need to test are x < -2, -2 < x < 4, and x > 4. By testing values from each interval in the inequality, we find that the inequality holds for the interval -2 < x < 4. Thus, the solution to the inequality is all values of x that are between -2 and 4, not including -2 and 4 themselves since the inequality is strictly less than 0.